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0.05 Tc 6.9718 0 0 6.6 92.12 553.1499 Tm (\)] )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 100.67 553.1499 Tm (= )Tj /T1_0 1 Tf 10 0 0 10 111.02 553.1499 Tm (4 )Tj 0.05 Tc 9.6349 0 0 9.5 119.06 553.1499 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 8.5621 0 0 9.5 138.41 553.1499 Tm ([G)Tj /T1_2 1 Tf 0.0155 Tc 6.4001 0 0 6.4001 148.36 551.35 Tm (p5 )Tj /T1_0 1 Tf 0.05 Tc 10.2072 0 0 9.5 157.2 553.1499 Tm (\(8)Tj 0 Tc 6.6 0 0 6.6 166.41 551.89 Tm (5)Tj 0.05 Tc 7.23 0 0 6.6 170.78 553.1499 Tm (\)] )Tj -0.035 Tc 9.7667 0 0 10 190.38 553.1499 Tm (24, )Tj -0.0301 Tc 9.5 0 0 9.5 205.97 553.1499 Tm (so )Tj /T1_1 1 Tf -0.0191 Tc 1.251 0 Td (R\(5, )Tj /T1_0 1 Tf -0.035 Tc 9.5491 0 0 10 238.08 553.1499 Tm (25\) )Tj /C0_0 1 Tf 0 Tc 5.5801 0 0 7.5601 254.17 553.1499 Tm <007E0020>Tj /T1_0 1 Tf -0.0202 Tc 10 0 0 10 263.84 553.1499 Tm (458. )Tj -0.035 Tc 9.5256 0 0 10 35.35 535.3199 Tm (\(6\) )Tj 0.0232 Tc 9.5 0 0 9.5 50.17 535.3199 Tm (Let )Tj /T1_2 1 Tf -0.035 Tc 7.9611 0 0 9.2 66.84 535.3199 Tm (P6 )Tj /T1_0 1 Tf 0 Tc 11.4 0 0 11.4 79.5 535.3199 Tm (= )Tj -0.0213 Tc 10 0 0 10 89.42 535.3199 Tm (443,96 )Tj 0 Tc 11.4 0 0 11.4 119.46 535.3199 Tm (= )Tj -0.035 Tc 9.3091 0 0 10 129.73 535.3199 Tm (2, )Tj 0.05 Tc 9.7524 0 0 9.5 140.48 535.3199 Tm (and )Tj 0 Tc 10.6 0 0 10.6 37.25 512.11 Tm (8)Tj 10 0 0 10 42.9 510.49 Tm (6 )Tj 13 0 0 13 49.97 512.11 Tm (= )Tj 0.05 Tc 10.008 0 0 10 60.07 512.11 Tm ({1,4,5,6,13,14,15,18,21,22,27,31,32,33,34,37,38,40,41,43,47,48,49,50, )Tj 0.0441 Tc 10 0 0 10 64.84 497.71 Tm (51,52,57,59,60,63,65,67,71,72,73,75,77, )Tj 0.0304 Tc 18.201 0 Td (78,89,90,92, )Tj -0.0038 Tc 5.61 0 Td (106,108, )Tj -0.035 Tc 9.8374 0 0 10 340.4 497.71 Tm (112, )Tj -0.0195 Tc 10 0 0 10 359.29 497.71 Tm (113, )Tj 0.0278 Tc -29.43 -1.44 Td (115,116,119,121,123,127,128,133,136,138,140, )Tj -0.0255 Tc 20.7 0 Td (145, )Tj 0.0103 Tc 1.926 0 Td (148,151,152, )Tj -0.035 Tc 9.9518 0 0 10 347.6 483.31 Tm (157, )Tj 0.0304 Tc 10 0 0 10 64.99 468.7299 Tm (159,166,168,169,170,172,173,174,175,176,179,181,182,191,194,195, )Tj -0.0315 Tc 0 -1.44 TD (199, )Tj -0.035 Tc 9.5198 0 0 10 84 454.33 Tm (202, )Tj 9.8518 0 0 10 102.36 454.33 Tm (204, )Tj 9.9625 0 0 10 121.26 454.33 Tm [(207, )-90(209, )]TJ 9.7412 0 0 10 159.42 454.33 Tm (210, )Tj -0.031 Tc 10 0 0 10 178.14 454.33 Tm (218, )Tj -0.035 Tc 9.9126 0 0 10 197.4 454.33 Tm (220}. )Tj 0.05 Tc 9.6317 0 0 9.5 35.38 429.31 Tm (Then )Tj /T1_1 1 Tf -0.035 Tc 7.7396 0 0 9.5 60.83 429.31 Tm ([Gpo )Tj /T1_3 1 Tf 0.0225 Tc 10.2 0 0 10.2 79.2 429.31 Tm (\(8)Tj /T1_0 1 Tf 0 Tc 10 0 0 10 88.44 428.05 Tm (6)Tj -0.035 Tc 7.9399 0 0 10 92.83 429.31 Tm (\)] )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 101.39 429.31 Tm (= )Tj /T1_0 1 Tf 10 0 0 10 111.48 429.31 Tm (6 )Tj 0.05 Tc 9.7524 0 0 9.5 119.6 429.31 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 7.9976 0 0 9.5 138.95 429.31 Tm ([Gpo )Tj /T1_3 1 Tf 0.0048 Tc 10.2 0 0 10.2 157.68 429.31 Tm (\(8)Tj /T1_0 1 Tf 0 Tc 10 0 0 10 166.74 428.05 Tm (6)Tj -0.035 Tc 8.5281 0 0 10 171.31 429.31 Tm (\)] )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 180.59 429.31 Tm (= )Tj /T1_0 1 Tf -0.0313 Tc 10 0 0 10 190.99 429.31 Tm (14, )Tj -0.0111 Tc 9.5 0 0 9.5 206.51 429.31 Tm (so )Tj /T1_1 1 Tf -0.0128 Tc 1.251 0 Td (R\(7, )Tj /T1_0 1 Tf -0.035 Tc 9.8188 0 0 10 238.7 429.31 Tm (15\) )Tj /C0_0 1 Tf 0 Tc 5.5801 0 0 7.7401 254.89 429.31 Tm <007E0020>Tj /T1_0 1 Tf -0.0202 Tc 10 0 0 10 264.56 429.31 Tm (444. )Tj -0.035 Tc 9.6928 0 0 10 36.07 411.49 Tm (\(7\) )Tj 0.0232 Tc 9.5 0 0 9.5 50.89 411.49 Tm (Let )Tj /T1_1 1 Tf -0.035 Tc 7.4531 0 0 8.5 67.41 411.49 Tm (P7 )Tj /T1_0 1 Tf -0.0249 Tc 10 0 0 10 90.14 411.49 Tm (461,97 )Tj 0 Tc 11.4 0 0 11.4 120.18 411.49 Tm (= )Tj -0.035 Tc 9.3091 0 0 10 130.27 411.49 Tm (2, )Tj 0.05 Tc 9.7524 0 0 9.5 141.02 411.49 Tm (and )Tj 0 Tc 9.9 0 0 9.9 42.31 388.81 Tm (8)Tj 10 0 0 10 48.31 387.19 Tm (7 )Tj 12.1 0 0 12.1 55.2 388.81 Tm (= )Tj 0.0428 Tc 10 0 0 10 64.93 388.81 Tm ({1,2,3,13, )Tj 0.0406 Tc 4.632 0 Td (14,20,21,22,23,28, )Tj 0.0358 Tc 8.471 0 Td (29,30,32,33,35,37,38,40,41,42, )Tj 0.0349 Tc 13.862 0 Td (44,45,46, )Tj 0.0444 Tc -26.46 -1.422 Td (48,50,52,55,57,60,61,63,66,68,69, )Tj 0.0158 Tc 15.419 0 Td (71,72,75, )Tj 0.0374 Tc 4.14 0 Td (78,82,86,90,99,102,108, )Tj 0.0283 Tc -19.536 -1.44 Td (113,117,118,119,122,123,124,127,128,129,134, )Tj -0.035 Tc 9.6086 0 0 10 277.77 360.19 Tm (135, )Tj -0.0167 Tc 10 0 0 10 296.29 360.19 Tm (136,139, )Tj -0.0135 Tc 3.654 0 Td (145, )Tj -0.0195 Tc 1.962 0 Td (148, )Tj 0.0283 Tc -28.206 -1.44 Td (152,153,155,162,163,167,169,170,173,175,177, )Tj 0.0207 Tc 20.754 0 Td (178,179,181,182,183, )Tj 0.03 Tc -20.754 -1.404 Td (186,187,188,192,194,196,199,201,204,206,211,218,222,226,228,229}. )Tj 0.05 Tc 9.5493 0 0 9.5 36.28 306.7299 Tm (Then )Tj /T1_1 1 Tf -0.035 Tc 8.5621 0 0 9.5 61.55 306.7299 Tm ([G)Tj /T1_2 1 Tf 0.0113 Tc 6.6 0 0 6.6 71.14 304.9299 Tm (p7 )Tj /T1_3 1 Tf 0.05 Tc 9.8912 0 0 9.8 79.93 306.7299 Tm (\(8)Tj /T1_0 1 Tf 0 Tc 10 0 0 10 89.17 305.47 Tm (7)Tj -0.035 Tc 7.3518 0 0 10 93.56 306.7299 Tm (\)] )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 102.11 306.7299 Tm (= )Tj /T1_0 1 Tf 10 0 0 10 112.2 306.7299 Tm (6 )Tj 0.05 Tc 9.7524 0 0 9.5 120.32 306.7299 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 8.5621 0 0 9.5 139.67 306.7299 Tm ([G)Tj /T1_2 1 Tf 0.0385 Tc 6.6 0 0 6.6 149.44 305.11 Tm (p7 )Tj /T1_3 1 Tf 0.0401 Tc 9.8 0 0 9.8 158.23 306.7299 Tm (\(8)Tj /T1_0 1 Tf 0 Tc 10 0 0 10 167.29 305.47 Tm (7)Tj -0.035 Tc 8.5281 0 0 10 172.03 306.7299 Tm (\)] )Tj 0 Tc 11.3 0 0 11.3 181.2 306.7299 Tm (= )Tj -0.0313 Tc 10 0 0 10 191.53 306.7299 Tm (15, )Tj -0.0301 Tc 9.5 0 0 9.5 207.23 306.7299 Tm (so )Tj /T1_1 1 Tf -0.0065 Tc 1.232 0 Td (R\(7, )Tj /T1_0 1 Tf -0.035 Tc 9.6677 0 0 10 239.43 306.7299 Tm (16\) )Tj /C0_0 1 Tf 0 Tc 5.5801 0 0 7.5601 255.43 306.7299 Tm <007E0020>Tj /T1_0 1 Tf -0.0262 Tc 10 0 0 10 265.1 306.7299 Tm (462. )Tj -0.035 Tc 9.3585 0 0 10 36.97 289.27 Tm (\(8\) )Tj 0.0232 Tc 9.5 0 0 9.5 51.43 289.27 Tm (Let )Tj /T1_2 1 Tf -0.035 Tc 7.9611 0 0 9.2 68.1 289.27 Tm (P8 )Tj /T1_0 1 Tf -0.0213 Tc 10 0 0 10 90.5 289.27 Tm (421,98 )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 120.47 289.27 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.3091 0 0 10 130.81 289.27 Tm (2, )Tj 0.05 Tc 9.8699 0 0 9.5 141.38 289.27 Tm (and )Tj 0 Tc 10.6 0 0 10.6 39.77 266.41 Tm (8)Tj 10 0 0 10 45.54 264.7899 Tm (8 )Tj 0.0203 Tc 1.705 0.162 Td ({1,4, )Tj 0.048 Tc 2.316 0 Td (7,13,21,22,24,29,34,35,36,37,40,44,46,47,48,52,53,54,56,60,62, )Tj 0.0401 Tc -1.837 -1.44 Td (67,71,76,79,80,81,82,84,90,91,92,93,99,100,103,108,109,111,113,114, )Tj 0.0278 Tc 0.013 -1.422 Td (116,118,121,126,129,135,136,140,141,142,144, )Tj 0.0217 Tc 20.754 0 Td (146,147,148,149,150, )Tj 0.0274 Tc -20.718 -1.44 Td (151,152,153,154,155,162,165,166,168,169,171, )Tj 0.0217 Tc 20.718 0 Td (173,176,177,180,181, )Tj -0.0012 Tc -20.736 -1.458 Td (183,185, )Tj 0.0245 Tc 3.762 0 Td (186,188,190,194,196, )Tj -0.035 Tc 9.723 0 0 10 200.18 208.81 Tm (197, )Tj 0.007 Tc 10 0 0 10 218.89 208.81 Tm (198,202,203, )Tj -0.035 Tc 9.6305 0 0 10 274.98 208.81 Tm (204, )Tj 9.7412 0 0 10 293.52 208.81 Tm (206, )Tj 9.1877 0 0 10 312.25 208.81 Tm (207, )Tj -0.0125 Tc 10 0 0 10 330.06 208.81 Tm (210}. )Tj 0.0412 Tc 9.5 0 0 9.5 37 183.7899 Tm (Then )Tj /T1_1 1 Tf -0.035 Tc 8.3909 0 0 9.5 62.09 183.7899 Tm ([G)Tj /T1_2 1 Tf 6.2176 0 0 6.6 71.67 181.81 Tm (pB )Tj /T1_3 1 Tf 0.05 Tc 9.8912 0 0 9.8 80.29 183.7899 Tm (\(8)Tj /T1_0 1 Tf 0 Tc 10 0 0 10 89.46 182.35 Tm (8)Tj -0.035 Tc 7.3518 0 0 10 93.92 183.7899 Tm (\)] )Tj 0 Tc 10 0 0 10 112.75 183.7899 Tm (7 )Tj 0.05 Tc 9.7524 0 0 9.5 120.68 183.7899 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 8.7334 0 0 9.5 140.03 183.7899 Tm ([G)Tj /T1_2 1 Tf 6.2176 0 0 6.6 149.79 181.99 Tm (pB )Tj /T1_3 1 Tf 0.0401 Tc 9.8 0 0 9.8 158.59 183.7899 Tm (\(8)Tj /T1_0 1 Tf 0 Tc 10 0 0 10 167.58 182.53 Tm (8)Tj -0.035 Tc 8.234 0 0 10 172.39 183.7899 Tm (\)] )Tj 0 Tc 11.4 0 0 11.4 181.56 183.7899 Tm (= )Tj -0.035 Tc 9.9045 0 0 10 192.08 183.7899 Tm (12, )Tj -0.0301 Tc 9.5 0 0 9.5 207.59 183.7899 Tm (so )Tj /T1_1 1 Tf -0.0065 Tc 1.232 0 Td (R\(8, )Tj /T1_0 1 Tf -0.035 Tc 9.5167 0 0 10 239.97 183.7899 Tm (13\) )Tj /C0_0 1 Tf 0 Tc 5.5801 0 0 7.5601 255.97 183.7899 Tm <007E0020>Tj /T1_0 1 Tf -0.0322 Tc 10 0 0 10 265.64 183.7899 Tm (422. )Tj -0.035 Tc 9.6928 0 0 10 37.51 165.7899 Tm (\(9\) )Tj 0.0138 Tc 9.5 0 0 9.5 52.33 165.7899 Tm (Let )Tj /T1_2 1 Tf -0.035 Tc 7.7952 0 0 9.2 68.82 165.7899 Tm (P9 )Tj /T1_0 1 Tf -0.0195 Tc 10 0 0 10 90.96 165.7899 Tm (617,99 )Tj 0 Tc 11.4 0 0 11.4 121.08 165.7899 Tm (= )Tj -0.035 Tc 9.8216 0 0 10 131.11 165.7899 Tm (3, )Tj 0.05 Tc 9.7524 0 0 9.5 141.92 165.7899 Tm (and )Tj 0 Tc 10.6 0 0 10.6 39.23 142.03 Tm (8)Tj 10 0 0 10 45.07 140.41 Tm (9 )Tj /T1_3 1 Tf 8.1 0 0 8.1 52.07 142.03 Tm (= )Tj /T1_0 1 Tf 0.0477 Tc 10 0 0 10 61.69 142.03 Tm ({1,3,4,8, )Tj 0.0147 Tc 4.11 0 Td (10,11, )Tj 0.0465 Tc 2.826 0 Td (14,23,25,26,27,28,32,33,34,35,36,37,38,46,47,49,55,62, )Tj 0.0407 Tc -6.439 -1.422 Td (65,75,79,81,82,85,86,87,89,90,91,94,98,99,108,110,112,113,115,116, )Tj 0.0274 Tc 0.013 -1.459 Td 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-0.0225 Tc 10 0 0 10 59.64 304.03 Tm (\(52\)] )Tj 0 Tc 3.33 0 Td (3 )Tj 0.013 Tc 0.794 0 Td (and )Tj /T1_2 1 Tf -0.035 Tc 8.3909 0 0 9.8 119.87 304.03 Tm ([G)Tj /T1_3 1 Tf -0.0126 Tc 6.4001 0 0 6.4001 129.46 302.41 Tm (p2 )Tj /T1_0 1 Tf 0.0034 Tc 9.8 0 0 9.8 138.07 304.03 Tm (\(8)Tj /T1_1 1 Tf 0 Tc 10 0 0 10 147 302.77 Tm (2)Tj -0.035 Tc 7.9399 0 0 10 151.33 304.03 Tm (\)] )Tj 9.7421 0 0 10 170.12 304.03 Tm (16, )Tj 9.991 0 0 10 185.26 304.03 Tm (so )Tj /T1_2 1 Tf -0.0147 Tc 9.8 0 0 9.8 197.69 304.03 Tm (R\( )Tj /T1_1 1 Tf 0.0231 Tc 10 0 0 10 208.94 304.03 Tm (4,17\) )Tj -0.035 Tc 4.0102 0 0 10 234.8 304.03 Tm (:::::: )Tj 9.9518 0 0 10 245 304.03 Tm (182. )Tj -0.0335 Tc 10 0 0 10 14.64 286.93 Tm (\(3\) )Tj 0.0341 Tc 1.554 0 Td (Let )Tj /T1_3 1 Tf -0.035 Tc 7.9611 0 0 8.9 47.76 286.93 Tm (P3 )Tj /T1_1 1 Tf -0.0134 Tc 10 0 0 10 70.86 286.93 Tm (277,93 )Tj 0 Tc 10.9 0 0 10.9 101.65 286.93 Tm (= )Tj -0.035 Tc 8.9895 0 0 10 111.48 286.93 Tm (5, )Tj 0.013 Tc 10 0 0 10 121.94 286.93 Tm (and )Tj 0.0422 Tc -9.364 -2.178 Td (53 )Tj 0.047 Tc 2.421 0 Td ({1,3,4,12,13,16,19,21,25,27,29,30,39,41,47,48,49,52,55,57,59,62, )Tj 0.0444 Tc 0.461 -1.476 Td (63,64,66,69,70,74,76,79,81,83,84,85,89,90, )Tj -0.035 Tc 9.9518 0 0 10 253.1 250.39 Tm (100, )Tj 0.0121 Tc 10 0 0 10 271.99 250.39 Tm (102,108,113,116, )Tj 0.0191 Tc -21.456 -1.458 Td (120,121,122,123,131}. )Tj 0.05 Tc 10.2902 0 0 10 14.49 211.51 Tm (Then )Tj /T1_2 1 Tf -0.035 Tc 8.3909 0 0 9.8 41.39 211.51 Tm ([G)Tj /T1_3 1 Tf 0.05 Tc 6.1947 0 0 5.8001 50.97 209.71 Tm (p3 )Tj /T1_1 1 Tf -0.018 Tc 10 0 0 10 59.82 211.51 Tm (\(53\)] )Tj 0 Tc 3.338 0 Td (4 )Tj 0.013 Tc 0.804 0 Td (and )Tj /T1_2 1 Tf -0.035 Tc 8.5621 0 0 9.8 120.05 211.51 Tm ([G)Tj /T1_3 1 Tf 0.05 Tc 6.1947 0 0 5.8001 129.63 209.89 Tm (p3 )Tj /T1_0 1 Tf 0.0401 Tc 9.6 0 0 9.6 138.25 211.51 Tm (\(8)Tj /T1_1 1 Tf 0 Tc 10 0 0 10 146.94 210.07 Tm (3)Tj -0.035 Tc 8.234 0 0 10 151.51 211.51 Tm (\)] )Tj 0 Tc 12.1 0 0 12.1 160.5 211.51 Tm (= )Tj -0.035 Tc 9.7421 0 0 10 170.3 211.51 Tm (15, )Tj 9.991 0 0 10 185.44 211.51 Tm (so )Tj /T1_2 1 Tf -0.0254 Tc 9.8 0 0 9.8 197.69 211.51 Tm (R\(5, )Tj /T1_1 1 Tf -0.035 Tc 9.9699 0 0 10 218.53 211.51 Tm (16\) )Tj 4.1355 0 0 10 234.98 211.51 Tm (:::::: )Tj 9.8518 0 0 10 245.1 211.51 Tm (278. )Tj 9.8599 0 0 10 15.18 194.23 Tm (\(4\) )Tj 0.0251 Tc 10 0 0 10 30.54 194.23 Tm (Let )Tj /T1_3 1 Tf -0.035 Tc 7.9611 0 0 9.2 48.12 194.23 Tm (P4 )Tj /T1_1 1 Tf -0.0026 Tc 10 0 0 10 70.8 194.23 Tm (379,94 )Tj -0.035 Tc 8.7919 0 0 10 111.73 194.23 Tm (2, )Tj 0.004 Tc 10 0 0 10 122.12 194.23 Tm (and )Tj -0.035 Tc 9.8625 0 0 10 19.12 171.55 Tm (54 )Tj 0 Tc 12.1 0 0 12.1 32.7 171.55 Tm (= )Tj 0.0452 Tc 10 0 0 10 43.33 171.55 Tm ({1,4,11,14,18,24,30,31,38,39,40,43,44,49,50,51,52,53,61,63,65,69,79, )Tj 0.0351 Tc 0.437 -1.422 Td (81,84,85,87,94,96,103,105,107,108,111,115,121, )Tj -0.0315 Tc 21.619 0 Td (128, )Tj 0.0061 Tc 1.908 0 Td (133,135,140,145, )Tj 0.0289 Tc -23.49 -1.404 Td (151,154,160,166,171,175,177,178,180,181,182,185,186}. )Tj 0.05 Tc 10.2902 0 0 10 14.85 118.63 Tm (Then )Tj /T1_2 1 Tf -0.035 Tc 8.3909 0 0 9.8 41.75 118.63 Tm ([G)Tj /T1_3 1 Tf 0.0155 Tc 6.4001 0 0 6.4001 51.34 117 Tm (p4 )Tj /T1_1 1 Tf -0.0225 Tc 10 0 0 10 60.18 118.63 Tm (\(54\)] )Tj 0 Tc 3.32 0 Td (4 )Tj 0.013 Tc 0.804 0 Td (and )Tj /T1_2 1 Tf -0.035 Tc 8.5621 0 0 9.8 120.23 118.63 Tm ([G)Tj /T1_3 1 Tf -0.0126 Tc 6.4001 0 0 6.4001 129.82 117.18 Tm (p4 )Tj /T1_1 1 Tf -0.035 Tc 9.88 0 0 10 138.48 118.63 Tm (\(54\)] )Tj /T1_0 1 Tf 0 Tc 8.1 0 0 8.1 160.61 118.63 Tm (= )Tj /T1_1 1 Tf -0.035 Tc 9.7421 0 0 10 170.48 118.63 Tm (19, )Tj 9.991 0 0 10 185.62 118.63 Tm (so )Tj /T1_2 1 Tf -0.0254 Tc 9.8 0 0 9.8 197.87 118.63 Tm (R\(5, )Tj /T1_1 1 Tf -0.035 Tc 9.8385 0 0 10 218.64 118.63 Tm (20\) )Tj 4.1355 0 0 10 235.16 118.63 Tm (:::::: )Tj -0.031 Tc 10 0 0 10 245.04 118.63 Tm (380. )Tj -0.035 Tc 9.8599 0 0 10 15.54 101.71 Tm (\(5\) )Tj 0.0251 Tc 10 0 0 10 30.9 101.71 Tm (Let )Tj /T1_3 1 Tf -0.035 Tc 7.9611 0 0 8.6 48.3 101.71 Tm (P5 )Tj /T1_1 1 Tf -0.0105 Tc 10 0 0 10 71.06 101.71 Tm (457,95 )Tj 0 Tc 10.9 0 0 10.9 102.01 101.71 Tm (= )Tj -0.035 Tc 9.4173 0 0 10 112.17 101.71 Tm (13, )Tj 0.013 Tc 10 0 0 10 126.98 101.71 Tm (and )Tj -0.035 Tc 9.8625 0 0 10 19.48 79.38 Tm (55 )Tj 0 Tc 12.9 0 0 12.9 33.06 79.38 Tm (= )Tj 0.0449 Tc 10 0 0 10 43.69 79.38 Tm ({1,3,11,12,13,18,20,22,26,32,35,44,45,46,49,52,54,55,56,58,61,62,63, )Tj -0.035 Tc 9.8149 0 0 10 48.32 65.17 Tm (70, )Tj 0.0373 Tc 10 0 0 10 62.53 65.17 Tm (76,82,85,86,89,92,94,97,99,103,104,105, )Tj 0.0169 Tc 18.192 0 Td (109,111,113,119,120,122, )Tj 0.0285 Tc -19.602 -1.458 Td (125,127,130,133,134,136,139,143,153,159,163,168, )Tj 0.0097 Tc 22.59 0 Td (170,172,173,175, )Tj -0.0315 Tc -22.572 -1.422 Td [(177, )-65(184, )]TJ 0.0258 Tc 3.816 0 Td (192,198,200,202,206,207,216,217,220,223,225,226}. )Tj -0.035 Tc 9.8721 0 0 10 182.89 14.23 Tm (87 )Tj ET endstream endobj 165 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 36064/Name/Im0/Subtype/Image/Type/XObject/Width 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)Tj 0.05 Tc 9.5074 0 0 9.4 155.57 435.97 Tm (subsets )Tj 0.0491 Tc 9.4 0 0 9.4 189.81 435.97 Tm (of )Tj -0.035 Tc 8.838 0 0 9.4 201.39 435.97 Tm ([1, )Tj /T1_2 1 Tf 7.3824 0 0 8.6 212.67 435.97 Tm (Tn] )Tj /T1_3 1 Tf -0.0086 Tc 9.4 0 0 9.4 227.24 435.97 Tm (for )Tj -0.0015 Tc 1.533 0 Td (cyclic )Tj 0.0482 Tc 2.759 0 Td (graphs )Tj 0.0108 Tc 3.293 0 Td (of )Tj 0.038 Tc 1.13 0 Td (order )Tj /T1_1 1 Tf 0.0111 Tc 8.7 0 0 8.7 334.19 435.97 Tm (p. )Tj /T1_3 1 Tf 0.0493 Tc 9.5 0 0 9.5 346.64 435.97 Tm (By )Tj 0.0092 Tc 9.4 0 0 9.4 362.59 435.97 Tm (\(4.3\) )Tj -0.035 Tc 9.2755 0 0 9.4 35.81 418.51 Tm (we )Tj 0.0306 Tc 9.4 0 0 9.4 51.29 418.51 Tm (reduce )Tj 0.05 Tc 9.4206 0 0 9.4 82.71 418.51 Tm (out )Tj 9.9612 0 0 9.4 100.88 418.51 Tm (at )Tj 0.0349 Tc 9.4 0 0 9.4 113.68 418.51 Tm (least )Tj /C0_0 1 Tf 0 Tc 3.8251 0 0 7.9201 138.25 418.51 Tm <00310054007E00740020>Tj /T1_3 1 Tf 0.05 Tc 9.5989 0 0 9.4 159.39 418.51 Tm (of )Tj 9.8457 0 0 9.4 171.98 418.51 Tm (amount )Tj 0.0491 Tc 9.4 0 0 9.4 209.07 418.51 Tm (of )Tj 0.05 Tc 9.4459 0 0 9.4 221.13 418.51 Tm (computation. )Tj 0.0051 Tc 9.4 0 0 9.4 284.51 418.51 Tm (In )Tj 0.0274 Tc 1.384 0 Td (many )Tj 0.0479 Tc 2.788 0 Td (cases )Tj 0.0491 Tc 2.834 0 Td (of )Tj /T1_1 1 Tf 0.05 Tc 9.3993 0 0 9.2 362.83 418.51 Tm (nt, )Tj -0.0118 Tc 9.9 0 0 9.9 375.9 418.51 Tm (t, )Tj /T1_3 1 Tf 0.05 Tc 9.5625 0 0 9.4 35.98 406.81 Tm (the )Tj 0.043 Tc 9.4 0 0 9.4 53.09 406.81 Tm (reduction )Tj -0.0179 Tc 4.588 0 Td (is )Tj 0.0162 Tc 1.07 0 Td (even )Tj 0.0275 Tc 2.386 0 Td (bigger )Tj 0.0295 Tc 3.126 0 Td (since )Tj -0.0308 Tc 2.636 0 Td (we )Tj 0.0045 Tc 1.648 0 Td (use )Tj 0.05 Tc 9.6991 0 0 9.4 215.62 406.81 Tm (the )Tj 0.0487 Tc 9.4 0 0 9.4 233.1 406.81 Tm (upper )Tj 0.05 Tc 9.6343 0 0 9.4 260.65 406.81 Tm (bound )Tj 0.03 Tc 9.4 0 0 9.4 290.97 406.81 Tm (of )Tj /T1_0 1 Tf -0.035 Tc 7.9754 0 0 12.9 302.9 406.81 Tm (ITVI )Tj /T1_3 1 Tf 0.05 Tc 9.5157 0 0 9.4 321.13 406.81 Tm (by )Tj 0.0225 Tc 9.4 0 0 9.4 336.49 406.81 Tm (\(4.3\). )Tj 0.05 Tc 9.7889 0 0 9.4 365.32 406.81 Tm (The )Tj 9.512 0 0 9.4 36.08 395.11 Tm (amount )Tj 0.0348 Tc 9.4 0 0 9.4 70.91 395.11 Tm (reduced )Tj 0.05 Tc 9.5533 0 0 9.4 106.11 395.11 Tm (out )Tj -0.035 Tc 9.3682 0 0 9.4 123.04 395.11 Tm (is )Tj 0.0408 Tc 9.4 0 0 9.4 132.57 395.11 Tm (considerably )Tj 0.0458 Tc 5.937 0 Td (large )Tj 0.0189 Tc 2.566 0 Td (if )Tj /T1_1 1 Tf 0 Tc 10.6 0 0 10.6 221.09 395.11 Tm (t )Tj /T1_3 1 Tf -0.0179 Tc 9.4 0 0 9.4 227.8 395.11 Tm (is )Tj 0.028 Tc 1.041 0 Td (relatively )Tj 0.0352 Tc 4.391 0 Td (small )Tj 0.0222 Tc 2.655 0 Td (with )Tj 0.05 Tc 9.611 0 0 9.4 324.71 395.11 Tm (respect )Tj 10.2589 0 0 9.4 358.89 395.11 Tm (to )Tj /T1_2 1 Tf 6.4478 0 0 6.1 370.92 395.11 Tm (Tn. )Tj /T1_3 1 Tf 0.0322 Tc 9.4 0 0 9.4 36.14 383.41 Tm (For )Tj 0.05 Tc 9.5625 0 0 9.4 54.16 383.41 Tm (the )Tj 0.0144 Tc 9.4 0 0 9.4 71.37 383.41 Tm (cases )Tj 0.0177 Tc 2.632 0 Td (which )Tj -0.035 Tc 9.1156 0 0 9.4 124.37 383.41 Tm (we )Tj 0.0471 Tc 9.4 0 0 9.4 139.22 383.41 Tm (are )Tj /C0_0 1 Tf 0 Tc 4.1221 0 0 7.5601 156.25 383.41 Tm <0069006E0074006500720065007300740065007E0020>Tj /T1_3 1 Tf 0.0434 Tc 9.4 0 0 9.4 202.42 383.41 Tm (in )Tj 0.026 Tc 1.309 0 Td (mostly, )Tj 0.05 Tc 9.4886 0 0 9.4 248.86 383.41 Tm (i.e.,m/12 )Tj /T1_0 1 Tf -0.035 Tc 5.9959 0 0 11.2 290.9 383.41 Tm (:s; )Tj /T1_1 1 Tf 0 Tc 10.4 0 0 10.4 301.92 383.41 Tm (t )Tj /T1_0 1 Tf -0.035 Tc 5.9959 0 0 11.2 309.8 383.41 Tm (:s; )Tj /T1_3 1 Tf 0.05 Tc 10.6179 0 0 9.4 320.38 383.41 Tm (m/2, )Tj 9.6991 0 0 9.4 346.48 383.41 Tm (the )Tj 10.0945 0 0 9.4 364.34 383.41 Tm (part )Tj 0.0379 Tc 9.4 0 0 9.4 35.99 371.53 Tm (reduced )Tj 0.05 Tc 9.686 0 0 9.4 71.37 371.53 Tm (out )Tj -0.035 Tc 9.0754 0 0 9.4 87.95 371.53 Tm (is )Tj 0.05 Tc 10.1984 0 0 9.4 96.92 371.53 Tm (at )Tj 0.0396 Tc 9.4 0 0 9.4 108.1 371.53 Tm (least )Tj -0.035 Tc 9.2824 0 0 9.4 130.19 371.53 Tm (50 )Tj 0.05 Tc 9.6041 0 0 9.4 142.54 371.53 Tm (to )Tj -0.035 Tc 9.1906 0 0 9.4 153.62 371.53 Tm (92 )Tj 0.05 Tc 9.5355 0 0 9.4 165.97 371.53 Tm (percent. )Tj 9.679 0 0 9.4 205.12 371.53 Tm (The )Tj 0.0406 Tc 9.4 0 0 9.4 224.45 371.53 Tm (reduction )Tj 0.0277 Tc 4.434 0 Td (comes )Tj 0.0161 Tc 2.986 0 Td (from )Tj 0.0483 Tc 2.346 0 Td (non-normalized )Tj 0.01 Tc -29.804 -1.245 Td (cyclic )Tj 0.0336 Tc 2.778 0 Td (graphs, )Tj 0.0224 Tc 3.521 0 Td (each )Tj 0.0491 Tc 2.241 0 Td (of )Tj 0.05 Tc 9.7359 0 0 9.4 127.24 359.83 Tm (them )Tj -0.035 Tc 9.3682 0 0 9.4 151.3 359.83 Tm (is )Tj 0.049 Tc 9.4 0 0 9.4 160.48 359.83 Tm (isomorphic )Tj 0.05 Tc 9.6041 0 0 9.4 210.22 359.83 Tm (to )Tj 0.0259 Tc 9.4 0 0 9.4 221.67 359.83 Tm (one )Tj 0.0108 Tc 1.857 0 Td (of )Tj 0.05 Tc 9.4259 0 0 9.4 249.46 359.83 Tm (the )Tj 0.0373 Tc 9.4 0 0 9.4 265.31 359.83 Tm (normalized )Tj 0.01 Tc 5.181 0 Td (cyclic )Tj 0.05 Tc 9.6818 0 0 9.4 340.48 359.83 Tm (graphs )Tj 0.0053 Tc 9.4 0 0 9.4 372.25 359.83 Tm (by )Tj 0.05 Tc 9.4407 0 0 9.4 36.46 348.13 Tm (Theorem )Tj -0.0154 Tc 9.4 0 0 9.4 77.11 348.13 Tm (3.1. )Tj -0.0146 Tc -2.282 -1.226 Td (Now )Tj -0.035 Tc 8.9557 0 0 9.4 77.57 336.61 Tm (we )Tj 0.0477 Tc 9.4 0 0 9.4 91.36 336.61 Tm (illustrate )Tj 0.05 Tc 9.4401 0 0 9.4 131.74 336.61 Tm (Algorithm )Tj -0.0046 Tc 9.4 0 0 9.4 178.34 336.61 Tm (4.1 )Tj 0.05 Tc 9.4612 0 0 9.4 194.57 336.61 Tm (with )Tj 9.8357 0 0 9.4 216.7 336.61 Tm (the )Tj -0.0046 Tc 9.4 0 0 9.4 233.54 336.61 Tm (following )Tj 0.0473 Tc 4.279 0 Td (three )Tj 0.0311 Tc 2.577 0 Td (examples. )Tj /T1_4 1 Tf 0.05 Tc 10.2084 0 0 9.5 36.48 311.41 Tm (Example )Tj /T1_5 1 Tf 0.0444 Tc 8.5 0 0 8.5 82.42 311.41 Tm (1. )Tj /T1_2 1 Tf 0.009 Tc 9.8 0 0 9.8 95.81 311.41 Tm (R\(3,5\) )Tj /T1_0 1 Tf -0.035 Tc 7.2152 0 0 10.2 127.74 311.41 Tm (2: )Tj /T1_3 1 Tf -0.0094 Tc 9.4 0 0 9.4 137.37 311.41 Tm (14 )Tj -0.0191 Tc 1.44 0 Td (\(see )Tj -0.0167 Tc 1.998 0 Td ([3]\). )Tj 0.0401 Tc -12.121 -1.838 Td (Let )Tj /T1_1 1 Tf 0 Tc 9.3 0 0 9.3 72.67 294.13 Tm (p )Tj /T1_0 1 Tf 8.1 0 0 8.1 80.51 294.13 Tm (= )Tj /T1_3 1 Tf -0.0148 Tc 9.4 0 0 9.4 90.57 294.13 Tm (13, )Tj /T1_1 1 Tf 0 Tc 8.9 0 0 8.9 105.41 294.13 Tm (9 )Tj /T1_3 1 Tf -0.035 Tc 9.0505 0 0 9.4 123.43 294.13 Tm (2. )Tj 0.0208 Tc 9.4 0 0 9.4 134.83 294.13 Tm (Select )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 162.24 294.13 Tm (t )Tj /T1_0 1 Tf 8.1 0 0 8.1 169.07 294.13 Tm (= )Tj /T1_3 1 Tf -0.035 Tc 9.0505 0 0 9.4 179.59 294.13 Tm (2. )Tj 0.0457 Tc 9.4 0 0 9.4 191.78 294.13 Tm (Consider )Tj 0.0145 Tc 4.309 0 Td (all )Tj 0.0369 Tc 1.395 0 Td (subsets )Tj 0.0243 Tc 3.548 0 Td (in )Tj -0.0058 Tc 1.19 0 Td ([0,5] )Tj /T1_0 1 Tf -0.035 Tc 5.4128 0 0 10.4 311.49 294.13 Tm (== )Tj /T1_3 1 Tf 8.6 0 0 10.3 321.13 294.13 Tm ({O, )Tj 0.05 Tc 10.5411 0 0 9.4 335.87 294.13 Tm (1,2,3,4, )Tj -0.035 Tc 9.1009 0 0 9.4 373.55 294.13 Tm (5} )Tj 0.035 Tc 9.4 0 0 9.4 36.59 282.61 Tm (satisfying )Tj 0.0065 Tc 4.809 0 Td (\(3.2-3\). )Tj 0.042 Tc 4.21 0 Td (Note )Tj 0.05 Tc 10.0691 0 0 9.4 146.5 282.61 Tm (that )Tj 10.6728 0 0 8 169.27 282.61 Tm (al )Tj /T1_0 1 Tf 0 Tc 11.1 0 0 11.1 185.4 282.61 Tm (< )Tj /T1_1 1 Tf 0.05 Tc 11.3688 0 0 10.4 198.85 282.61 Tm (m/\(t )Tj /T1_3 1 Tf 0 Tc 10.4 0 0 10.4 223.44 282.61 Tm (-)Tj -0.035 Tc 9.1661 0 0 9.4 234.22 282.61 Tm (1\) )Tj 0 Tc 11.4 0 0 11.4 248.16 282.61 Tm (= )Tj -0.035 Tc 9.1252 0 0 9.4 261.07 282.61 Tm (6. )Tj 9.1049 0 0 9.4 278.97 282.61 Tm (We )Tj 0.0109 Tc 9.4 0 0 9.4 296.99 282.61 Tm (have )Tj /T1_0 1 Tf -0.035 Tc 10.6257 0 0 12.9 320.83 282.61 Tm (IWI )Tj /T1_3 1 Tf 0 Tc 11.4 0 0 11.4 343.2 282.61 Tm (= )Tj 9.4 0 0 9.4 356.63 282.61 Tm (5 )Tj 0.05 Tc 9.6349 0 0 9.4 367.1 282.61 Tm (and )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 37.15 271.27 Tm (B)Tj /T1_2 1 Tf 5.6 0 0 5.6 44.05 269.65 Tm (r)Tj 0.348 0.289 Td (\225 )Tj /T1_3 1 Tf 12.1 0 0 12.1 52.32 271.27 Tm (= )Tj -0.035 Tc 8.327 0 0 10.3 63.56 271.27 Tm ({O, )Tj /T1_1 1 Tf -0.0325 Tc 10.5 0 0 10.5 77.52 271.27 Tm (r} )Tj /T1_3 1 Tf 0 Tc 8.7 0 0 8.7 90.67 271.27 Tm (E )Tj /T1_1 1 Tf 0.05 Tc 10.2006 0 0 10 100.43 271.27 Tm (W, )Tj /T1_2 1 Tf 0 Tc 5.9001 0 0 5.9001 117.14 271.27 Tm (T )Tj /T1_3 1 Tf 8.7 0 0 8.7 126.31 271.27 Tm (E )Tj 0.0105 Tc 9.4 0 0 9.4 136.21 271.27 Tm ([1,5]. )Tj 0.0448 Tc 2.969 0 Td (Hence )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 194.74 271.27 Tm (S )Tj /T1_3 1 Tf 12.1 0 0 12.1 205.32 271.27 Tm (= )Tj /T1_1 1 Tf -0.01 Tc 10.3 0 0 10.3 216.87 271.27 Tm ({1,2T}. )Tj /T1_3 1 Tf 0.05 Tc 9.5282 0 0 9.4 253.18 271.27 Tm (There )Tj 0.0279 Tc 9.4 0 0 9.4 281.78 271.27 Tm (are )Tj -0.0326 Tc 1.723 0 Td (five )Tj 0.05 Tc 9.8563 0 0 9.4 316.28 271.27 Tm (parameter )Tj 0.0221 Tc 9.4 0 0 9.4 364.01 271.27 Tm (sets: )Tj 0.05 Tc 9.9228 0 0 9.4 37.03 259.57 Tm ({1,2},{1,4},{1,5},{1,3},{1,6}. )Tj 9.9631 0 0 9.4 177.63 259.57 Tm (When )Tj /T1_2 1 Tf 0 Tc 5.9001 0 0 5.9001 207.32 259.57 Tm (T )Tj /T1_3 1 Tf 11.4 0 0 11.4 216.66 259.57 Tm (= )Tj -0.0237 Tc 9.4 0 0 9.4 228.13 259.57 Tm (3, )Tj 0.0004 Tc 1.248 0 Td (i.e., )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 259.01 259.57 Tm (S )Tj /T1_0 1 Tf 8.1 0 0 8.1 269.33 259.57 Tm (= )Tj /T1_3 1 Tf 0.0379 Tc 9.4 0 0 9.4 281.5 259.57 Tm ({1,5}, )Tj -0.035 Tc 8.6358 0 0 9.4 311.21 259.57 Tm (we )Tj 0.025 Tc 9.4 0 0 9.4 325.52 259.57 Tm (find )Tj 0.05 Tc 10.7257 0 0 9.4 346.83 259.57 Tm (that )Tj 9.6991 0 0 9.4 369.16 259.57 Tm (the )Tj 0.0177 Tc 9.4 0 0 9.4 36.81 248.23 Tm (clique )Tj 0.0488 Tc 3.053 0 Td (number )Tj 0.03 Tc 3.84 0 Td (of )Tj /T1_2 1 Tf 0.0048 Tc 9.3 0 0 9.3 113.67 248.23 Tm (Gp\(S\) )Tj /T1_3 1 Tf -0.035 Tc 9.3682 0 0 9.4 144.46 248.23 Tm (is )Tj 0 Tc 9.4 0 0 9.4 155.46 248.23 Tm (2 )Tj 0.05 Tc 10.1049 0 0 9.4 164.78 248.23 Tm (and )Tj 9.9723 0 0 9.4 185.74 248.23 Tm (the )Tj 0.0366 Tc 9.4 0 0 9.4 204.22 248.23 Tm (independence )Tj 0.05 Tc 9.4373 0 0 9.4 264.95 248.23 Tm (number )Tj 0.03 Tc 9.4 0 0 9.4 301.23 248.23 Tm (of )Tj /T1_2 1 Tf 0.0145 Tc 9.3 0 0 9.3 313.29 248.23 Tm (Gp\(S\) )Tj /T1_3 1 Tf -0.035 Tc 9.3682 0 0 9.4 344.8 248.23 Tm (is )Tj -0.0262 Tc 9.4 0 0 9.4 356 248.23 Tm (4. )Tj -0.0257 Tc 1.767 0 Td (So )Tj /T1_2 1 Tf 0.009 Tc 9.8 0 0 9.8 36.95 236.71 Tm (R\(3,5\) )Tj /T1_0 1 Tf -0.035 Tc 7.6807 0 0 10.3 68.52 236.71 Tm (2: )Tj /T1_3 1 Tf -0.034 Tc 9.4 0 0 9.4 78.51 236.71 Tm (14. )Tj 0.042 Tc 1.705 0 Td (Note )Tj 0.05 Tc 10.0691 0 0 9.4 117.52 236.71 Tm (that )Tj 9.6221 0 0 9.4 138.05 236.71 Tm (without )Tj 0.0427 Tc 9.4 0 0 9.4 174.24 236.71 Tm (using )Tj 0.0373 Tc 2.756 0 Td (normalized )Tj 0.0061 Tc 5.181 0 Td (cyclic )Tj 0.0304 Tc 2.835 0 Td (graphs, )Tj -0.035 Tc 8.4759 0 0 9.4 308.69 236.71 Tm (we )Tj 0.05 Tc 9.4859 0 0 9.4 321.83 236.71 Tm (would )Tj 0.049 Tc 9.4 0 0 9.4 351.17 236.71 Tm (need )Tj 0.05 Tc 9.6041 0 0 9.4 374.2 236.71 Tm (to )Tj 0.031 Tc 9.4 0 0 9.4 36.95 225.55 Tm (search )Tj 0.001 Tc 3.067 0 Td (for )Tj 0.05 Tc 9.5322 0 0 9.4 80.72 225.55 Tm (an )Tj 0.0088 Tc 9.4 0 0 9.4 93.5 225.55 Tm (effective )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 130.85 225.55 Tm (S )Tj /T1_3 1 Tf 0.0161 Tc 9.4 0 0 9.4 140.3 225.55 Tm (from )Tj 0.0288 Tc 2.407 0 Td (15 )Tj 0.05 Tc 9.5644 0 0 9.4 175.9 225.55 Tm (subsets )Tj 9.9854 0 0 9.8 210.37 225.55 Tm ({I, )Tj -0.0019 Tc 9.4 0 0 9.4 224.58 225.55 Tm (2}, )Tj 0.0237 Tc 9.8 0 0 9.8 239 225.55 Tm ({I, )Tj -0.0024 Tc 9.4 0 0 9.4 252.25 225.55 Tm (3}, )Tj -0.009 Tc 1.504 0 Td (... )Tj 0 Tc 0.885 0 Td (, )Tj -0.035 Tc 9.3562 0 0 9.4 279.16 225.55 Tm ({5, )Tj -0.0182 Tc 9.4 0 0 9.4 292.2 225.55 Tm (6}. )Tj /T1_4 1 Tf 0.05 Tc 10.1196 0 0 9.5 37.2 208.27 Tm (Example )Tj 0.0108 Tc 9.5 0 0 9.5 82.74 208.27 Tm (2. )Tj /T1_2 1 Tf 0.05 Tc 9.2203 0 0 8.9 96.18 208.27 Tm (R\( )Tj /T1_3 1 Tf 9.536 0 0 9.4 107.42 208.27 Tm (4,4\) )Tj /T1_0 1 Tf -0.035 Tc 7.4479 0 0 10.2 127.92 208.27 Tm (2: )Tj /T1_3 1 Tf 0.0097 Tc 9.4 0 0 9.4 137.73 208.27 Tm (18 )Tj -0.0191 Tc 1.44 0 Td (\(see )Tj -0.0215 Tc 2.017 0 Td ([3]\). )Tj 0.0401 Tc -12.121 -1.819 Td (Let )Tj /T1_1 1 Tf 0 Tc 9.3 0 0 9.3 72.67 191.17 Tm (p )Tj /T1_0 1 Tf 8.7 0 0 8.7 80.68 191.17 Tm (= )Tj /T1_3 1 Tf -0.0053 Tc 9.4 0 0 9.4 90.57 191.17 Tm (17, )Tj /T1_2 1 Tf 0 Tc 8.6 0 0 8.6 104.95 191.17 Tm (9 )Tj /T1_3 1 Tf -0.035 Tc 9.2907 0 0 9.4 123.01 191.17 Tm (3. )Tj 0.0208 Tc 9.4 0 0 9.4 134.47 191.17 Tm (Select )Tj /T1_1 1 Tf 0 Tc 10.6 0 0 10.6 161.33 191.17 Tm (t )Tj /T1_0 1 Tf 8.1 0 0 8.1 168.17 191.17 Tm (= )Tj /T1_3 1 Tf -0.035 Tc 9.0039 0 0 9.4 178.7 191.17 Tm (4. )Tj 0.043 Tc 9.4 0 0 9.4 190.7 191.17 Tm (Consider )Tj 0.0145 Tc 4.289 0 Td (all )Tj 0.0401 Tc 1.337 0 Td (subsets )Tj 0.0051 Tc 3.51 0 Td (in )Tj -0.0058 Tc 1.152 0 Td ([0,7] )Tj 0.0414 Tc 2.251 0 Td (satisfying )Tj 0.0229 Tc 4.636 0 Td (\(3.2-3\). )Tj 0.042 Tc -33.495 -1.264 Td (Note )Tj 0.05 Tc 10.1785 0 0 9.4 59.56 179.29 Tm (that )Tj /T1_2 1 Tf 9.8294 0 0 8 79.44 179.29 Tm (al )Tj /T1_3 1 Tf 0 Tc 11.2 0 0 11.2 91.74 179.29 Tm (< )Tj /T1_1 1 Tf 0.05 Tc 12.7001 0 0 9.9 101.28 179.29 Tm (m/\(t-l\) )Tj /T1_0 1 Tf 0 Tc 8.1 0 0 8.1 141.35 179.29 Tm (= )Tj /T1_3 1 Tf 0.05 Tc 9.8667 0 0 9.4 151.21 179.29 Tm (8/3, )Tj 0.0195 Tc 9.4 0 0 9.4 171.28 179.29 Tm (i.e., )Tj 0.05 Tc 10.9099 0 0 8 189.25 179.29 Tm (al )Tj 10.0841 0 0 8 202.07 179.29 Tm (:; )Tj -0.035 Tc 9.3091 0 0 9.4 211.99 179.29 Tm (2. )Tj -0.0006 Tc 9.4 0 0 9.4 223.53 179.29 Tm (We )Tj 0.0109 Tc 1.687 0 Td (have )Tj /T1_2 1 Tf -0.035 Tc 9.9073 0 0 13.2 260.84 179.29 Tm (IWI )Tj /T1_0 1 Tf 0 Tc 8.1 0 0 8.1 279.23 179.29 Tm (= )Tj /T1_3 1 Tf -0.034 Tc 9.4 0 0 9.4 289.11 179.29 Tm (18. )Tj 0.05 Tc 9.4566 0 0 9.4 304.84 179.29 Tm (There )Tj 9.4959 0 0 9.4 332 179.29 Tm (are )Tj 0.0475 Tc 9.4 0 0 9.4 347.48 179.29 Tm (eighteen )Tj 0.05 Tc 9.5688 0 0 9.4 37.45 167.95 Tm (parameter )Tj 0.0193 Tc 9.4 0 0 9.4 82.49 167.95 Tm (sets. )Tj 0.0226 Tc 2.365 0 Td (For )Tj 0.0186 Tc 1.79 0 Td (simplicity, )Tj -0.0116 Tc 4.838 0 Td (we )Tj 0.0332 Tc 1.571 0 Td (use )Tj 0.0044 Tc 1.789 0 Td (0123 )Tj 0.05 Tc 9.6041 0 0 9.4 221.2 167.95 Tm (to )Tj 0.036 Tc 9.4 0 0 9.4 232.65 167.95 Tm (denote )Tj -0.035 Tc 8.1905 0 0 10.3 263.37 167.95 Tm ({O, )Tj 0.0408 Tc 9.4 0 0 9.4 277.59 167.95 Tm (1,2, )Tj -0.0024 Tc 1.862 0 Td (3}. )Tj 0.05 Tc 9.459 0 0 9.4 311.14 167.95 Tm (The )Tj 9.4042 0 0 9.4 330.56 167.95 Tm (eighteen )Tj 0.0367 Tc 9.4 0 0 9.4 369.37 167.95 Tm (pa\255)Tj 0.05 Tc 9.4604 0 0 9.4 37.43 156.43 Tm (rameter )Tj 0.0261 Tc 9.4 0 0 9.4 78.35 156.43 Tm (sets )Tj 0.0279 Tc 2.588 0 Td (are )Tj 0.05 Tc 9.4173 0 0 9.4 124.1 156.43 Tm (0123,0124,0125,0126,0127,0134,0135,0136,0137,0145,0146, )Tj 0.046 Tc 9.4 0 0 9.4 37.34 144.73 Tm (0147,0156,0157,0167,0246,0247,0257. )Tj 0.05 Tc 9.5362 0 0 9.4 206.07 144.73 Tm (When )Tj /T1_1 1 Tf 0 Tc 6.6 0 0 6.6 236.39 144.73 Tm (T )Tj /T1_3 1 Tf 11.4 0 0 11.4 247.44 144.73 Tm (= )Tj -0.0148 Tc 9.4 0 0 9.4 261.21 144.73 Tm (16, )Tj /T1_1 1 Tf 0.05 Tc 9.2606 0 0 9.2 279.97 144.73 Tm (Br )Tj /T1_3 1 Tf -0.035 Tc 7.6445 0 0 10.3 311.09 144.73 Tm ({O, )Tj 0.05 Tc 9.932 0 0 9.4 324.48 144.73 Tm (2,4, )Tj 0.0106 Tc 9.4 0 0 9.4 343.5 144.73 Tm (6}, )Tj /T1_1 1 Tf 0 Tc 9.2 0 0 9.2 362.51 144.73 Tm (S )Tj /T1_3 1 Tf 0.0079 Tc 9.4 0 0 9.4 37.6 133.21 Tm ({3\260, )Tj -0.035 Tc 6.8488 0 0 9.4 55.92 133.21 Tm (13)Tj 0 Tc 6.4001 0 0 6.4001 63.14 136.81 Tm (2)Tj -0.035 Tc 5.8733 0 0 11 67.48 133.21 Tm (1, )Tj 6.4459 0 0 9.4 74.84 133.21 Tm (13)Tj 0 Tc 6.4001 0 0 6.4001 81.69 136.81 Tm (4)Tj -0.035 Tc 5.3139 0 0 10.8 86.22 133.21 Tm (1, )Tj 6.6473 0 0 9.4 93.01 133.21 Tm (13)Tj 0 Tc 6.4001 0 0 6.4001 100 136.81 Tm (6)Tj /T1_0 1 Tf -0.035 Tc 7.2813 0 0 11.2 104.53 133.21 Tm (1} )Tj /T1_3 1 Tf 0.042 Tc 9.8 0 0 9.8 129.74 133.21 Tm ({I, )Tj -0.035 Tc 9.0505 0 0 9.4 143.59 133.21 Tm (2, )Tj 9.0039 0 0 9.4 152.6 133.21 Tm (4, )Tj 0.0254 Tc 9.4 0 0 9.4 161.47 133.21 Tm (8}, )Tj -0.0116 Tc 1.894 0 Td (we )Tj -0.0005 Tc 1.733 0 Td (find )Tj 0.05 Tc 10.2879 0 0 9.4 216.69 133.21 Tm (that )Tj 0.0422 Tc 9.4 0 0 9.4 239.38 133.21 Tm (the )Tj 0.0215 Tc 1.869 0 Td (clique )Tj 0.0335 Tc 3.111 0 Td (number )Tj 0.05 Tc 10.0163 0 0 9.4 321.56 133.21 Tm (of )Tj /T1_2 1 Tf 0.0193 Tc 9.3 0 0 9.3 334.89 133.21 Tm (Gp\(S\) )Tj /T1_3 1 Tf -0.035 Tc 9.3682 0 0 9.4 366.76 133.21 Tm (is )Tj 0 Tc 9.4 0 0 9.4 378.07 133.21 Tm (3 )Tj 0.05 Tc 9.5174 0 0 9.4 37.7 122.22 Tm (and )Tj 9.5625 0 0 9.4 56.14 122.22 Tm (the )Tj 0.0314 Tc 9.4 0 0 9.4 72.82 122.22 Tm (independence )Tj 0.0488 Tc 6.269 0 Td (number )Tj 0.05 Tc 9.5989 0 0 9.4 166.95 122.22 Tm (of )Tj /T1_2 1 Tf 0.0242 Tc 9.3 0 0 9.3 178.29 122.22 Tm (Gp\(S\) )Tj /T1_3 1 Tf -0.035 Tc 9.3682 0 0 9.4 208.54 122.22 Tm (is )Tj /C0_0 1 Tf 0 Tc 2.1001 0 0 7.0201 218.53 122.22 Tm <007E007E002E0020>Tj /T1_3 1 Tf 0.0356 Tc 9.4 0 0 9.4 230.8 122.22 Tm (Note )Tj 0.05 Tc 10.0691 0 0 9.4 253.96 122.22 Tm (that )Tj 0.0472 Tc 9.4 0 0 9.4 274.85 122.22 Tm (without )Tj 0.0235 Tc 3.793 0 Td (using )Tj 0.05 Tc 9.4014 0 0 9.4 335.87 122.22 Tm (normalized )Tj -0.0027 Tc 9.5 0 0 9.5 37.71 104.22 Tm (cyclic )Tj 0.0219 Tc 2.767 0 Td (graphs, )Tj -0.035 Tc 8.9557 0 0 9.8 97.55 104.22 Tm (we )Tj -0.0083 Tc 9.8 0 0 9.8 111.59 104.22 Tm (would )Tj 0.0092 Tc 2.865 0 Td (need )Tj 0.05 Tc 10.0407 0 0 9.8 162.34 104.22 Tm (to )Tj 0.0312 Tc 9.8 0 0 9.8 174.46 104.22 Tm (search )Tj -0.0232 Tc 3.089 0 Td (for )Tj 0.05 Tc 9.8988 0 0 9.8 219.86 104.22 Tm (an )Tj 0.0018 Tc 9.5 0 0 9.5 233.18 104.22 Tm (effective )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 270.53 104.22 Tm (S )Tj /T1_3 1 Tf -0.035 Tc 9.6921 0 0 9.8 280.69 104.22 Tm (from )Tj 0.05 Tc 17.225 0 0 9.8 304.35 104.22 Tm (\(:\) )Tj 0 Tc 12.1 0 0 12.1 327.9 104.22 Tm (= )Tj -0.0203 Tc 9.8 0 0 9.8 338.66 104.22 Tm (70 )Tj 0.0312 Tc 1.355 0 Td (subsets )Tj 0.0157 Tc 10.3 0 0 10.3 37.92 86.94 Tm ({I, )Tj -0.035 Tc 8.7919 0 0 10.3 51.79 86.94 Tm (2, )Tj 9.2907 0 0 10.3 60.55 86.94 Tm (3, )Tj 9.7578 0 0 10.3 69.8 86.94 Tm (4}, )Tj 0.007 Tc 10.3 0 0 10.3 83.64 86.94 Tm ({I, )Tj -0.035 Tc 9.0505 0 0 10.3 97.33 86.94 Tm (2, )Tj 9.2907 0 0 10.3 106.27 86.94 Tm (3, )Tj 9.9218 0 0 10.3 115.24 86.94 Tm (5}, )Tj 9.884 0 0 10.3 129.4 86.94 Tm (... )Tj 0 Tc 10.3 0 0 10.3 137.36 86.94 Tm (, )Tj -0.035 Tc 9.6845 0 0 10.3 141.62 86.94 Tm ({5, )Tj 0.05 Tc 9.7453 0 0 9.4 155.04 86.94 Tm (6,7, )Tj -0.035 Tc 10.0899 0 0 10.3 173.52 86.94 Tm (8}. )Tj /T1_4 1 Tf 0.05 Tc 10.0752 0 0 9.5 37.92 69.49 Tm (Example )Tj 0.0301 Tc 9.5 0 0 9.5 83.12 69.49 Tm (3. )Tj /T1_2 1 Tf -0.0172 Tc 10 0 0 10 96.52 69.49 Tm (R\( )Tj /T1_3 1 Tf 0.048 Tc 9.4 0 0 9.4 107.78 69.49 Tm (4,10\) )Tj /T1_0 1 Tf -0.035 Tc 7.6807 0 0 10.3 132.96 69.49 Tm (2: )Tj /T1_3 1 Tf -0.0266 Tc 9.4 0 0 9.4 142.75 69.49 Tm (80 )Tj -0.0063 Tc 1.443 0 Td (\(see )Tj -0.0167 Tc 2.036 0 Td ([7]\). )Tj 0.0401 Tc -12.619 -1.762 Td (Let )Tj /T1_1 1 Tf 0 Tc 8.3 0 0 8.3 75.52 52.93 Tm (p )Tj /T1_3 1 Tf 10.5 0 0 10.5 86.35 52.93 Tm (= )Tj -0.0287 Tc 9.4 0 0 9.4 99.08 52.93 Tm (79, )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 116.12 52.93 Tm (9 )Tj /T1_3 1 Tf -0.035 Tc 9.2907 0 0 9.4 140.29 52.93 Tm (3. )Tj 0.0323 Tc 9.4 0 0 9.4 157.33 52.93 Tm (Select )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 187.62 52.93 Tm (t )Tj /T1_3 1 Tf -0.0148 Tc 9.4 0 0 9.4 210.63 52.93 Tm (13. )Tj 0.032 Tc 2.341 0 Td (Consider )Tj 0.037 Tc 9 0 0 9 274.41 52.93 Tm (all )Tj 0.0241 Tc 9.4 0 0 9.4 289.13 52.93 Tm (subsets )Tj 0.05 Tc 9.7676 0 0 9.4 323.56 52.93 Tm (in )Tj 0.0179 Tc 9.4 0 0 9.4 337.63 52.93 Tm ([0,38] )Tj 0.05 Tc 9.4208 0 0 9.4 367.25 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BT /T1_0 1 Tf 0.0361 Tc 3 Tr 9.3 0 0 9.3 16.63 545.77 Tm (\(2\) )Tj 0.0185 Tc 1.91 0 Td (Select )Tj 0 Tc 3.086 0 Td (a )Tj 0.0474 Tc 0.983 0 Td (subset )Tj 0.0197 Tc 3.295 0 Td (of )Tj -0.035 Tc 8.838 0 0 9.3 115.35 545.77 Tm ([0, )Tj /T1_1 1 Tf 0.0399 Tc 8 0 0 8 126.83 545.77 Tm (rn )Tj /T1_0 1 Tf -0.035 Tc 7.9274 0 0 9.3 148.41 545.77 Tm (1] )Tj 0.05 Tc 9.6485 0 0 9.3 160.01 545.77 Tm (with )Tj /T1_2 1 Tf 0 Tc 9.9 0 0 9.9 183.66 545.77 Tm (t )Tj /T1_0 1 Tf 0.0405 Tc 9.3 0 0 9.3 191.78 545.77 Tm (elements )Tj 0.05 Tc 10.1785 0 0 9.3 232.54 545.77 Tm (that )Tj 0.0365 Tc 9.3 0 0 9.3 254.57 545.77 Tm (satisfies )Tj -0.0027 Tc 4.125 0 Td (\(3.2-3\). )Tj 0.0418 Tc 3.917 0 Td (Denote )Tj 0.05 Tc 9.4259 0 0 9.3 34.54 534.61 Tm (the )Tj 0.0388 Tc 9.3 0 0 9.3 51.17 534.61 Tm (set )Tj 0.039 Tc 1.669 0 Td (of )Tj 0.0236 Tc 1.215 0 Td (such )Tj 0.0488 Tc 2.342 0 Td (subsets )Tj 0.0161 Tc 3.634 0 Td (by )Tj /T1_2 1 Tf 0.05 Tc 10.2006 0 0 9.6 147.05 534.61 Tm (W. )Tj /T1_0 1 Tf 0.0142 Tc 9.3 0 0 9.3 165.75 534.61 Tm (We )Tj 0.0307 Tc 1.891 0 Td (list )Tj 0.0199 Tc 1.78 0 Td (all )Tj 0.05 Tc 9.5625 0 0 9.3 213.82 534.61 Tm (the )Tj 9.3367 0 0 9.3 230.63 534.61 Tm (subsets )Tj 9.5456 0 0 9.3 264.7 534.61 Tm (in )Tj /T1_2 1 Tf 0 Tc 9.6 0 0 9.6 277.21 534.61 Tm (W )Tj /T1_0 1 Tf 0.0243 Tc 9.3 0 0 9.3 291.33 534.61 Tm (according )Tj 0.05 Tc 9.8224 0 0 9.3 333.88 534.61 Tm (to )Tj 0.0396 Tc 9.3 0 0 9.3 346.12 534.61 Tm (the )Tj 0.0305 Tc -33.51 -1.239 Td (lexicographic )Tj 0.044 Tc 6.192 0 Td (order )Tj 0.05 Tc 9.3902 0 0 9.3 116.91 523.09 Tm (of )Tj 0.0463 Tc 9.3 0 0 9.3 128.14 523.09 Tm (their )Tj 0.0429 Tc 2.391 0 Td (elements. )Tj 0.0385 Tc 4.731 0 Td (Assume )Tj /T1_1 1 Tf 0.05 Tc 11.5446 0 0 10.9 82.79 500.05 Tm (Ih )Tj /T1_2 1 Tf 10.6988 0 0 10.3 107.44 500.05 Tm ([O,t-I], )Tj 12.5903 0 0 10.3 155.07 500.05 Tm (Br={ajE[O,m-I]:jE[O,t-I]}. )Tj /T1_0 1 Tf 0.0373 Tc 9.3 0 0 9.3 34.75 476.29 Tm (Set )Tj /T1_1 1 Tf 0 Tc 8.2 0 0 8.2 51.4 476.29 Tm (r )Tj /T1_3 1 Tf -0.035 Tc 7.8553 0 0 8.5 68.87 476.29 Tm (1. )Tj /T1_0 1 Tf 0.0361 Tc 9.3 0 0 9.3 17.17 464.77 Tm (\(3\) )Tj /T1_3 1 Tf 0.05 Tc 12.1279 0 0 9.1 34.41 464.77 Tm (If )Tj /T1_2 1 Tf 0 Tc 9.9 0 0 9.9 44.22 464.77 Tm (r )Tj /T1_3 1 Tf 10.7 0 0 10.7 52.03 464.77 Tm (> )Tj /T1_1 1 Tf -0.035 Tc 10.1981 0 0 12.7 61.93 464.77 Tm (IWI, )Tj /T1_0 1 Tf 0.0354 Tc 9.3 0 0 9.3 83.03 464.77 Tm (stop. )Tj 0.0411 Tc 2.617 0 Td (Otherwise )Tj 0.05 Tc 9.6192 0 0 9.3 152.55 464.77 Tm (construct )Tj /T1_1 1 Tf 0 Tc 8.6 0 0 8.6 195.66 464.77 Tm (S )Tj /T1_3 1 Tf 8.1 0 0 8.1 204.53 464.77 Tm (= )Tj /T1_1 1 Tf -0.035 Tc 9.4696 0 0 12.7 215.32 464.77 Tm ({Iga)Tj 0 Tc 4.5001 0 0 4.5001 231.47 467.29 Tm (j )Tj /T1_3 1 Tf 12.9 0 0 12.9 235.8 464.77 Tm [(I )150(: )]TJ /T1_2 1 Tf -0.035 Tc 6.3348 0 0 6.9001 246.29 464.77 Tm ({},j )Tj /T1_0 1 Tf 0 Tc 8.7 0 0 8.7 258.43 464.77 Tm (E )Tj /T1_1 1 Tf 8.6 0 0 8.6 267.37 464.77 Tm (B)Tj 12.7 0 0 12.7 275.1 463.51 Tm (r)Tj 0.417 0.099 Td (} )Tj /T1_0 1 Tf 0.05 Tc 9.5174 0 0 9.3 287.72 464.77 Tm (and )Tj /T1_1 1 Tf 0.0335 Tc 8.6 0 0 8.6 305.93 464.77 Tm (Gp\(S\). )Tj /T1_0 1 Tf 0.0361 Tc 9.3 0 0 9.3 17.17 453.07 Tm (\(4\) )Tj 0.05 Tc 9.4573 0 0 9.3 34.82 453.07 Tm (Construct )Tj /T1_1 1 Tf 0 Tc 8.6 0 0 8.6 79.98 453.07 Tm (A )Tj /T1_3 1 Tf 8.1 0 0 8.1 90.05 453.07 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 7.3586 0 0 10.5 100.5 453.07 Tm ({:r: )Tj 0 Tc 10.5 0 0 10.5 113.67 453.07 Tm (: )Tj /T1_1 1 Tf -0.035 Tc 9.596 0 0 11.9 119.72 453.07 Tm (Ixl )Tj /T1_3 1 Tf 0 Tc 7.8001 0 0 7.8001 133.2 453.07 Tm (E )Tj /T1_1 1 Tf 0.05 Tc 9.2694 0 0 8.6 142.19 453.07 Tm (S} )Tj /T1_0 1 Tf 0.0485 Tc 9.3 0 0 9.3 156.51 453.07 Tm (according )Tj 0.05 Tc 9.3858 0 0 9.3 200.68 453.07 Tm (to )Tj 0.0157 Tc 9.3 0 0 9.3 213.37 453.07 Tm (\(4.1\). )Tj -0.0002 Tc 2.914 0 Td (Use )Tj 0 Tc 2.004 0 Td (a )Tj 0.05 Tc 9.4004 0 0 9.3 267.03 453.07 Tm (depth-first )Tj 0.0213 Tc 9.3 0 0 9.3 314.87 453.07 Tm (search )Tj -0.02 Tc 3.157 0 Td (\(see )Tj -0.035 Tc 9.2784 0 0 9.6 35.24 441.73 Tm ([10]\) )Tj 0.0383 Tc 9.3 0 0 9.3 56.5 441.73 Tm (to )Tj -0.0011 Tc 1.211 0 Td (find )Tj /T1_1 1 Tf -0.035 Tc 8.8314 0 0 10.1 87.29 441.73 Tm ([A] )Tj /T1_0 1 Tf -0.0216 Tc 9.3 0 0 9.3 101.96 441.73 Tm (for )Tj 0.05 Tc 9.5625 0 0 9.3 116.26 441.73 Tm (the )Tj 0.04 Tc 9.3 0 0 9.3 132.4 441.73 Tm (induced )Tj 0.05 Tc 9.5089 0 0 9.3 167.45 441.73 Tm (sub-graph )Tj /T1_1 1 Tf -0.035 Tc 9.755 0 0 10.1 212.84 441.73 Tm (Gp[A] )Tj /T1_0 1 Tf 0.05 Tc 9.3902 0 0 9.3 240.39 441.73 Tm (of )Tj /T1_1 1 Tf -0.0187 Tc 10.1 0 0 10.1 250.99 441.73 Tm (Gp\(S\). )Tj /T1_3 1 Tf 0.05 Tc 12.1279 0 0 9.1 284.61 441.73 Tm (If )Tj /T1_1 1 Tf -0.035 Tc 8.9837 0 0 10.1 294.83 441.73 Tm ([A] )Tj /C0_0 1 Tf 0 Tc 5.4001 0 0 7.5601 309.79 441.73 Tm <007E0020>Tj /T1_0 1 Tf -0.0013 Tc 8.7 0 0 8.7 318.7 441.73 Tm (ql )Tj 0.05 Tc 13.0458 0 0 9.6 328.89 441.73 Tm (-1, )Tj 0.0194 Tc 9.3 0 0 9.3 347.81 441.73 Tm (set )Tj -0.035 Tc 4.3169 0 0 6.2 34.87 430.03 Tm ('T' )Tj /T1_1 1 Tf 0 Tc 8.2 0 0 8.2 52.3 430.03 Tm (r )Tj /T1_3 1 Tf 12.9 0 0 12.9 59.01 430.03 Tm (+ )Tj /T1_0 1 Tf 9.3 0 0 9.3 68.8 430.03 Tm (1 )Tj 0.05 Tc 9.5174 0 0 9.3 76.4 430.03 Tm (and )Tj 0.0018 Tc 9.3 0 0 9.3 94.78 430.03 Tm (go )Tj 0.05 Tc 9.6041 0 0 9.3 107.62 430.03 Tm (to )Tj 0.0053 Tc 9.3 0 0 9.3 119.77 430.03 Tm (\(3\). )Tj 0.0361 Tc -10.994 -1.239 Td (\(5\) )Tj 0.05 Tc 9.4573 0 0 9.3 35 418.51 Tm (Construct )Tj /T1_1 1 Tf 0 Tc 11.2 0 0 11.2 80.53 418.51 Tm (A )Tj /T1_0 1 Tf 0.034 Tc 9.3 0 0 9.3 91.53 418.51 Tm (according )Tj 0.05 Tc 9.3858 0 0 9.3 135.16 418.51 Tm (to )Tj 0.0196 Tc 9.3 0 0 9.3 147.85 418.51 Tm (\(4.1\). )Tj 0.0288 Tc 3.069 0 Td (Use )Tj 0 Tc 2.101 0 Td (a )Tj 0.0492 Tc 0.91 0 Td (depth-first )Tj 0.05 Tc 9.4678 0 0 9.3 252.41 418.51 Tm (search )Tj 0.0383 Tc 9.3 0 0 9.3 283.66 418.51 Tm (to )Tj -0.0011 Tc 1.308 0 Td (find )Tj /T1_1 1 Tf -0.035 Tc 7.1737 0 0 11.2 316.07 418.51 Tm ([AJ )Tj /T1_0 1 Tf 0.0074 Tc 9.3 0 0 9.3 331.1 418.51 Tm (for )Tj 0.0492 Tc 1.654 0 Td (the )Tj 0.04 Tc -33.49 -1.258 Td (induced )Tj 0.05 Tc 9.3031 0 0 9.3 70.79 406.81 Tm (sub-graph )Tj /T1_1 1 Tf -0.035 Tc 9.755 0 0 10.1 115.82 406.81 Tm (Gp[A] )Tj /T1_0 1 Tf 0.039 Tc 9.3 0 0 9.3 143.91 406.81 Tm (of )Tj /T1_1 1 Tf -0.0294 Tc 10.1 0 0 10.1 155.05 406.81 Tm (Gp\(S\). )Tj /T1_3 1 Tf 0.05 Tc 12.1279 0 0 9.1 189.75 406.81 Tm (If )Tj /T1_1 1 Tf -0.035 Tc 9.136 0 0 10.1 200.69 406.81 Tm ([A] )Tj /C0_0 1 Tf 0 Tc 5.5801 0 0 8.46 216.73 406.81 Tm <007E0020>Tj /T1_2 1 Tf -0.035 Tc 7.5763 0 0 9 227.12 406.81 Tm (q2 )Tj /T1_0 1 Tf 9.2294 0 0 9.3 248.44 406.81 Tm (1, )Tj 0.0484 Tc 9.3 0 0 9.3 259.43 406.81 Tm (set )Tj /T1_2 1 Tf 0 Tc 9 0 0 9 275.4 406.81 Tm (T )Tj /T1_0 1 Tf 12 0 0 12 284.16 406.81 Tm (= )Tj /T1_1 1 Tf 7.9001 0 0 7.9001 294.59 406.81 Tm (r )Tj /T1_3 1 Tf 12.2 0 0 12.2 301.84 406.81 Tm (+ )Tj /T1_0 1 Tf 9.3 0 0 9.3 311.8 406.81 Tm (1 )Tj 0.05 Tc 9.3999 0 0 9.3 319.22 406.81 Tm (and )Tj -0.035 Tc 9.2814 0 0 9.3 338.14 406.81 Tm (go )Tj 0.0383 Tc 9.3 0 0 9.3 351.16 406.81 Tm (to )Tj /T1_3 1 Tf -0.035 Tc 9.1371 0 0 9.6 35.48 395.47 Tm (\(3\) )Tj 0 Tc 9.6 0 0 9.6 47.62 395.47 Tm (. )Tj /T1_0 1 Tf 0.0361 Tc 9.3 0 0 9.3 17.71 383.95 Tm (\(6\) )Tj 0.0347 Tc 1.89 0 Td (Stop. )Tj 0.0365 Tc 0.003 -1.819 Td (Note )Tj 0.05 Tc 10.0691 0 0 9.3 58.66 367.03 Tm (that )Tj 0.0255 Tc 9.3 0 0 9.3 79.48 367.03 Tm (if )Tj 0.0492 Tc 0.994 0 Td (the )Tj 0.05 Tc 9.3519 0 0 9.3 105.2 367.03 Tm (algorithm )Tj 9.3643 0 0 9.3 148.73 367.03 Tm (stops )Tj 10.4356 0 0 9.3 173.95 367.03 Tm (at )Tj 9.5516 0 0 9.3 186.17 367.03 Tm (step )Tj 0.0246 Tc 9.3 0 0 9.3 207.43 367.03 Tm (\(6\), )Tj 0.0234 Tc 1.995 0 Td (from )Tj 0.05 Tc 9.3615 0 0 9.3 248.81 367.03 Tm (steps )Tj 0.0168 Tc 9.3 0 0 9.3 274.57 367.03 Tm (\(4\) )Tj 0.05 Tc 9.3999 0 0 9.3 290.24 367.03 Tm (and )Tj -0.0205 Tc 9.3 0 0 9.3 309.49 367.03 Tm (\(5\), )Tj -0.035 Tc 9.1156 0 0 9.3 326.51 367.03 Tm (we )Tj 0.0049 Tc 9.3 0 0 9.3 341.09 367.03 Tm (have )Tj /T1_1 1 Tf -0.035 Tc 9.745 0 0 10.1 15.65 355.33 Tm ([A] )Tj /T1_0 1 Tf 0 Tc 11.1 0 0 11.1 31.26 355.33 Tm (+ )Tj 9.3 0 0 9.3 41.17 355.33 Tm (2 )Tj -0.035 Tc 6.7855 0 0 11.7 49.51 355.33 Tm (:s; )Tj 0.05 Tc 8.8149 0 0 8.7 59.68 355.33 Tm (ql )Tj 9.5174 0 0 9.3 72.08 355.33 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 8.9837 0 0 10.4 91.61 355.33 Tm ([A] )Tj /T1_0 1 Tf 0 Tc 11.1 0 0 11.1 106.14 355.33 Tm (+ )Tj 9.3 0 0 9.3 115.69 355.33 Tm (2 )Tj -0.035 Tc 7.0044 0 0 11.7 124.2 355.33 Tm (:s; )Tj /T1_2 1 Tf 8.0748 0 0 9 134.59 355.33 Tm (q2; )Tj /T1_0 1 Tf 0.0456 Tc 9.3 0 0 9.3 149.56 355.33 Tm (therefore )Tj /T1_2 1 Tf 0.05 Tc 9.8844 0 0 9 191.05 355.33 Tm (R\(ql, )Tj -0.035 Tc 8.94 0 0 9 215.05 355.33 Tm (q2\) )Tj /C0_0 1 Tf 0 Tc 5.7601 0 0 8.46 231.31 355.33 Tm <007E0020>Tj /T1_2 1 Tf 9 0 0 9 241.5 355.33 Tm (p )Tj /T1_0 1 Tf 11.1 0 0 11.1 249.42 355.33 Tm (+ )Tj /T1_3 1 Tf -0.035 Tc 8.1087 0 0 8.5 259.3 355.33 Tm (1. )Tj /T1_0 1 Tf 0.0345 Tc 9.3 0 0 9.3 272.35 355.33 Tm (Since )Tj -0.0005 Tc 2.795 0 Td (finding )Tj 0 Tc 3.388 0 Td (a )Tj -0.0085 Tc 0.891 0 Td (lower )Tj 0.05 Tc 9.9688 0 0 9.3 15.13 344.35 Tm (bound )Tj -0.035 Tc 9.0754 0 0 9.3 45.47 344.35 Tm (is )Tj 0 Tc 9.3 0 0 9.3 54.45 344.35 Tm (a )Tj 0.0175 Tc 0.794 0 Td (difficult )Tj 0.0497 Tc 3.727 0 Td (problem )Tj -0.012 Tc 3.956 0 Td (for )Tj 0.0405 Tc 1.531 0 Td (larger )Tj /T1_2 1 Tf 0.05 Tc 9.5475 0 0 9 174.36 344.35 Tm (ql, )Tj -0.035 Tc 8.8044 0 0 9 187.69 344.35 Tm (q2, )Tj /T1_0 1 Tf 0.05 Tc 9.6991 0 0 9.3 201.94 344.35 Tm (the )Tj 9.4783 0 0 9.3 218.24 344.35 Tm (algorithm )Tj 9.5295 0 0 9.3 261.88 344.35 Tm (mostly )Tj 0.0442 Tc 9.3 0 0 9.3 293.27 344.35 Tm (stops )Tj 0.0459 Tc 2.578 0 Td (at )Tj 0.05 Tc 9.5516 0 0 9.3 327.83 344.35 Tm (step )Tj -0.0316 Tc 9.3 0 0 9.3 348.19 344.35 Tm (\(3\) )Tj 0.0171 Tc -35.805 -1.219 Td (for )Tj 0.05 Tc 9.4259 0 0 9.3 31.3 333.01 Tm (the )Tj 0.018 Tc 9.3 0 0 9.3 47.97 333.01 Tm (chosen )Tj /T1_1 1 Tf 0 Tc 8 0 0 8 78.33 333.01 Tm (p )Tj /T1_0 1 Tf 0.0485 Tc 9.3 0 0 9.3 87.39 333.01 Tm (and )Tj /T1_2 1 Tf -0.0146 Tc 9.6 0 0 9.6 105.91 333.01 Tm (t. )Tj /T1_0 1 Tf 0.05 Tc 9.5493 0 0 9.3 117.46 333.01 Tm (Then )Tj -0.035 Tc 8.9557 0 0 9.3 142.73 333.01 Tm (we )Tj 0.0434 Tc 9.3 0 0 9.3 156.95 333.01 Tm (need )Tj 0.05 Tc 9.8224 0 0 9.3 180.16 333.01 Tm (to )Tj 9.4499 0 0 9.3 192.5 333.01 Tm (alter )Tj /T1_1 1 Tf 0 Tc 8 0 0 8 214.95 333.01 Tm (p )Tj /T1_0 1 Tf 0.05 Tc 9.5174 0 0 9.3 223.82 333.01 Tm (and )Tj /T1_2 1 Tf 0 Tc 9.6 0 0 9.6 242.89 333.01 Tm (t )Tj /T1_0 1 Tf 0.05 Tc 9.3236 0 0 9.3 249.94 333.01 Tm (in )Tj 9.9669 0 0 9.3 261.4 333.01 Tm (step )Tj -0.0219 Tc 9.3 0 0 9.3 283.75 333.01 Tm (\(1\) )Tj 0.05 Tc 9.3999 0 0 9.3 298.88 333.01 Tm (and )Tj 9.3726 0 0 9.3 317.33 333.01 Tm (repeat )Tj 0.0492 Tc 9.3 0 0 9.3 346.66 333.01 Tm (the )Tj 0.05 Tc 9.6468 0 0 9.3 15.2 321.49 Tm (algorithm )Tj 0.0306 Tc 9.3 0 0 9.3 59.85 321.49 Tm (again. )Tj 0.05 Tc 9.3287 0 0 9.3 35.4 309.79 Tm (In )Tj 9.344 0 0 9.3 47.39 309.79 Tm (step )Tj 0.0053 Tc 9.3 0 0 9.3 68.65 309.79 Tm (\(1\), )Tj 0.0473 Tc 1.9 0 Td (instead )Tj 0.05 Tc 9.3902 0 0 9.3 119.25 309.79 Tm (of )Tj 0 Tc 9.3 0 0 9.3 130.41 309.79 Tm (a )Tj 0.0148 Tc 0.872 0 Td (given )Tj 0.0413 Tc 2.697 0 Td (value )Tj 0.05 Tc 9.3902 0 0 9.3 189.27 309.79 Tm (of )Tj /T1_2 1 Tf 0.0041 Tc 9.6 0 0 9.6 200.23 309.79 Tm (t, )Tj /T1_0 1 Tf -0.035 Tc 9.2755 0 0 9.3 210.05 309.79 Tm (we )Tj 0.05 Tc 9.3195 0 0 9.3 224.8 309.79 Tm (may )Tj 9.6741 0 0 9.3 245.87 309.79 Tm (run )Tj 9.3742 0 0 9.3 263.78 309.79 Tm (from )Tj 0 Tc 9.3 0 0 9.3 287.59 309.79 Tm (2 )Tj 0.05 Tc 9.3858 0 0 9.3 295.72 309.79 Tm (to )Tj /T1_2 1 Tf -0.035 Tc 9.0765 0 0 16.9 307.39 309.79 Tm (rn )Tj /T1_0 1 Tf 9.2002 0 0 9.3 318.86 309.79 Tm (for )Tj 0.0393 Tc 9.3 0 0 9.3 333.27 309.79 Tm (all )Tj 0.0396 Tc 1.459 0 Td (the )Tj 0.0332 Tc -35.678 -1.258 Td (choices )Tj 0.039 Tc 3.619 0 Td (of )Tj /T1_1 1 Tf 0.0355 Tc 8.3 0 0 8.3 59.99 298.09 Tm (t. )Tj /T1_0 1 Tf 0.05 Tc 9.3287 0 0 9.3 71.76 298.09 Tm (In )Tj 9.302 0 0 9.3 83.97 298.09 Tm (our )Tj 0.0303 Tc 9.3 0 0 9.3 101.24 298.09 Tm (experience, )Tj 0.0375 Tc 5.362 0 Td (choosing )Tj /T1_2 1 Tf -0.035 Tc 11.9177 0 0 16.9 191.27 298.09 Tm (rn/I2 )Tj /T1_0 1 Tf 7.0044 0 0 11.7 217.8 298.09 Tm (:s; )Tj /T1_1 1 Tf 0 Tc 8.3 0 0 8.3 228.29 298.09 Tm (t )Tj /T1_0 1 Tf -0.035 Tc 7.0044 0 0 11.7 235.62 298.09 Tm (:s; )Tj 0.05 Tc 10.4756 0 0 9.3 246.22 298.09 Tm (m/2 )Tj 9.8313 0 0 9.3 268.01 298.09 Tm (has )Tj 0.0338 Tc 9.3 0 0 9.3 286.11 298.09 Tm (often )Tj 0.0013 Tc 2.66 0 Td (worked. )Tj -0.0061 Tc 3.947 0 Td (All )Tj 0.05 Tc 10.2456 0 0 9.3 15.63 286.93 Tm (ten )Tj 0.021 Tc 9.3 0 0 9.3 33.28 286.93 Tm (values )Tj 0.05 Tc 9.3902 0 0 9.3 62.01 286.93 Tm (of )Tj /T1_2 1 Tf 0 Tc 9.9 0 0 9.9 73.32 286.93 Tm (t )Tj /T1_0 1 Tf 0.0218 Tc 9.3 0 0 9.3 80.46 286.93 Tm (used )Tj -0.006 Tc 2.372 0 Td (in )Tj 0.05 Tc 9.4259 0 0 9.3 114.1 286.93 Tm (the )Tj 9.317 0 0 9.3 130.69 286.93 Tm (proof )Tj 9.3902 0 0 9.3 155.79 286.93 Tm (of )Tj 9.5796 0 0 9.3 167.32 286.93 Tm (Theorem )Tj /T1_4 1 Tf -0.0229 Tc 8.5 0 0 8.5 209.14 286.93 Tm (1.1 )Tj /T1_0 1 Tf 0.0444 Tc 9.3 0 0 9.3 224.91 286.93 Tm (are )Tj 0.0327 Tc 1.782 0 Td (in )Tj 0.0424 Tc 1.265 0 Td (this )Tj 0.0405 Tc 2.053 0 Td (range. )Tj 0.0108 Tc 3.403 0 Td (For )Tj 0 Tc 1.795 0 Td (a )Tj 0.0245 Tc 0.853 0 Td (given )Tj /T1_2 1 Tf -0.0118 Tc 9.9 0 0 9.9 353.76 286.93 Tm (t, )Tj /T1_0 1 Tf 0.049 Tc 9.3 0 0 9.3 15.39 275.95 Tm (all )Tj 0.05 Tc 9.4259 0 0 9.3 29.68 275.95 Tm (the )Tj 0.0456 Tc 9.3 0 0 9.3 45.41 275.95 Tm (subsets )Tj 0.0327 Tc 3.547 0 Td (in )Tj 0.05 Tc 10.7751 0 0 9.3 89.6 275.95 Tm (Ware )Tj 9.3393 0 0 9.3 117.99 275.95 Tm (determined )Tj 0.0354 Tc 9.3 0 0 9.3 167.77 275.95 Tm (by )Tj 0.05 Tc 9.6554 0 0 9.3 180.94 275.95 Tm (step )Tj 0.0246 Tc 9.3 0 0 9.3 201.67 275.95 Tm (\(2\). )Tj -0.0245 Tc 2.041 0 Td (We )Tj 0.05 Tc 9.3296 0 0 9.3 236.78 275.95 Tm (estirnate )Tj /T1_1 1 Tf -0.035 Tc 9.9073 0 0 12.7 276.5 275.95 Tm (IWI )Tj /T1_0 1 Tf 0.0354 Tc 9.3 0 0 9.3 294.67 275.95 Tm (by )Tj 0.0299 Tc 1.41 0 Td (the )Tj 0.0006 Tc 1.637 0 Td (following )Tj 0.05 Tc 9.4403 0 0 9.3 15.64 264.61 Tm (theorem. )Tj /T1_5 1 Tf 10.4219 0 0 9.3 15.55 239.59 Tm (Theorem )Tj 9.7166 0 0 9.3 63.11 239.59 Tm (4.2. )Tj /T1_1 1 Tf 0 Tc 8 0 0 8 85.92 239.59 Tm (W )Tj 0.0481 Tc 1.646 0 Td (satisfies )Tj 0.05 Tc 8.2422 0 0 8 135.05 239.59 Tm (the )Tj 8.7606 0 0 8 150.91 239.59 Tm (following )Tj 8.2025 0 0 8 192.12 239.59 Tm (estimates: )Tj /T1_0 1 Tf 0.0362 Tc 9.6 0 0 9.6 16.27 217.63 Tm (\(a\) )Tj /T1_1 1 Tf -0.035 Tc 9.6533 0 0 12.7 42.32 217.63 Tm (IWI )Tj /T1_3 1 Tf 0.05 Tc 7.1664 0 0 6.1 88.09 217.63 Tm (=1 )Tj /T1_2 1 Tf -0.035 Tc 14.6113 0 0 16.9 105.19 217.63 Tm (\(rn+t )Tj 8.2451 0 0 16.9 146.56 217.63 Tm (:--=-2)Tj /T1_1 1 Tf 0.05 Tc 7.1069 0 0 6.2 163.89 222.31 Tm (a1)Tj /T1_2 1 Tf -0.0202 Tc 16.9 0 0 16.9 173.9 217.63 Tm (\(t-1\)\); )Tj /T1_3 1 Tf 0.0129 Tc 9.6 0 0 9.6 16.39 191.17 Tm (\(b\) )Tj /T1_1 1 Tf 0.0093 Tc 12.7 0 0 12.7 42.99 191.17 Tm (IWI/\(7\):S;;k. )Tj /T1_2 1 Tf 0.01 Tc 8.9 0 0 8.9 16.45 166.33 Tm (Pr'oof: )Tj /T1_0 1 Tf 0.0162 Tc 9.3 0 0 9.3 46.51 166.33 Tm (\(a\) )Tj 0.05 Tc 9.3177 0 0 9.3 60.62 166.33 Tm (From )Tj 0.0157 Tc 9.3 0 0 9.3 85.39 166.33 Tm (\(3.2\), )Tj -0.035 Tc 9.2755 0 0 9.3 109.43 166.33 Tm (we )Tj 0.0113 Tc 9.3 0 0 9.3 123.11 166.33 Tm (have )Tj 0 Tc 2.289 0 Td (1 )Tj -0.035 Tc 7.0044 0 0 11.7 151.74 166.33 Tm (:s; )Tj /T1_3 1 Tf 0.05 Tc 10.0677 0 0 7.7 161.36 166.33 Tm (al )Tj /T1_0 1 Tf -0.035 Tc 7.2233 0 0 11.7 174.06 166.33 Tm (:s; )Tj 8.8617 0 0 14.2 185.73 166.33 Tm ([7_-1)Tj 0 Tc 14.2 0 0 14.2 202.73 170.29 Tm (1)Tj -0.035 Tc 12.6415 0 0 14.2 207.41 166.33 Tm (]. )Tj 0.05 Tc 9.3436 0 0 9.3 219.38 166.33 Tm (By )Tj 0.0274 Tc 9.3 0 0 9.3 234.07 166.33 Tm (\(3.3\), )Tj -0.035 Tc 8.9557 0 0 9.3 259.01 166.33 Tm (we )Tj 0.0371 Tc 9.3 0 0 9.3 272.51 166.33 Tm (have )Tj /T1_1 1 Tf 0.05 Tc 6.9489 0 0 6.2 294.21 166.33 Tm (a1 )Tj /T1_3 1 Tf 0.0375 Tc 7.7 0 0 7.7 304.49 166.33 Tm (-{},o )Tj /T1_0 1 Tf 0 Tc 11.4 0 0 11.4 323.22 166.33 Tm (= )Tj /T1_3 1 Tf 0.05 Tc 9.844 0 0 7.7 333.26 166.33 Tm (al )Tj /T1_0 1 Tf 0.0485 Tc 9.3 0 0 9.3 345.15 166.33 Tm (and )Tj /T1_1 1 Tf 0.05 Tc 6.0284 0 0 6 16.05 152.47 Tm (\(},j )Tj /T1_3 1 Tf 0 Tc 6 0 0 6 27.49 152.47 Tm (-)Tj /T1_1 1 Tf 0.05 Tc 11.7063 0 0 6 36.03 152.47 Tm (aj-l )Tj 6.791 0 0 6 67.42 152.47 Tm (a1 )Tj /T1_3 1 Tf 0 Tc 12.2 0 0 12.2 78.1 152.47 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 7.3592 0 0 6 86.56 152.47 Tm (Cj, )Tj 0 Tc 8.5 0 0 8.5 98.95 152.47 Tm (j )Tj /T1_0 1 Tf 12 0 0 12 106.32 152.47 Tm (= )Tj 0.05 Tc 9.4906 0 0 9.3 116.22 152.47 Tm (2,3, )Tj -0.015 Tc 9.3 0 0 9.3 134.63 152.47 Tm (... )Tj 0 Tc 0.876 0 Td (, )Tj /T1_2 1 Tf 9.9 0 0 9.9 146.58 152.47 Tm (t )Tj /T1_3 1 Tf 0.05 Tc 11.5413 0 0 8.5 151.82 152.47 Tm (-1, )Tj /T1_0 1 Tf 0.0392 Tc 9.3 0 0 9.3 170.27 152.47 Tm (where )Tj /T1_1 1 Tf 0.05 Tc 6.8706 0 0 6 197.82 152.47 Tm (Cj )Tj /T1_3 1 Tf -0.035 Tc 7.9134 0 0 10 209.1 152.47 Tm (2: )Tj /T1_0 1 Tf 9.0857 0 0 9.3 219.15 152.47 Tm (0. )Tj 0.0286 Tc 9.3 0 0 9.3 230.72 152.47 Tm (Defining )Tj /T1_1 1 Tf 0.05 Tc 6.326 0 0 6 268.93 152.47 Tm (Ct )Tj /T1_0 1 Tf 0 Tc 12 0 0 12 280.02 152.47 Tm (= )Tj /T1_1 1 Tf 0.05 Tc 6.2561 0 0 6 289.75 152.47 Tm (Tn )Tj /T1_3 1 Tf 13.1085 0 0 8.5 308.1 152.47 Tm (1-)Tj /T1_1 1 Tf 7.325 0 0 6 321.83 152.47 Tm (CLt-l )Tj /C0_0 1 Tf 0 Tc 5.5801 0 0 7.2001 343.63 152.47 Tm <007E0020>Tj /T1_0 1 Tf -0.035 Tc 8.8261 0 0 9.3 352.89 152.47 Tm (0, )Tj -0.0186 Tc 9.3 0 0 9.3 16.19 140.05 Tm (we )Tj 0.0113 Tc 1.626 0 Td (have )Tj /T1_2 1 Tf -0.035 Tc 9.7351 0 0 10.3 53.56 140.05 Tm (L:;=2 )Tj /T1_1 1 Tf 0.05 Tc 6.8706 0 0 6 78.3 140.05 Tm (Cj )Tj /T1_0 1 Tf 0 Tc 9.3 0 0 9.3 98.98 140.05 Tm [(m )-143(-)-670(1 )-8(-)]TJ /T1_2 1 Tf -0.035 Tc 7.1746 0 0 10.3 135.04 140.05 Tm (CL1\(t )Tj /T1_0 1 Tf 0 Tc 10.3 0 0 10.3 153.96 140.05 Tm (-)Tj 0.0168 Tc 9.3 0 0 9.3 163.12 140.05 Tm (1\). )Tj 0.0279 Tc 1.675 0 Td (Hence )Tj /T1_1 1 Tf -0.035 Tc 9.9073 0 0 12.7 207.92 140.05 Tm (IWI )Tj /T1_0 1 Tf -0.0305 Tc 9.3 0 0 9.3 226.54 140.05 Tm (is )Tj 0.05 Tc 9.5625 0 0 9.3 236.32 140.05 Tm (the )Tj 9.4269 0 0 9.3 252.77 140.05 Tm (same )Tj 0.0307 Tc 9.3 0 0 9.3 277.65 140.05 Tm (as )Tj 0.05 Tc 9.4259 0 0 9.3 289.42 140.05 Tm (the )Tj 0.0365 Tc 9.3 0 0 9.3 305.63 140.05 Tm (number )Tj 0.039 Tc 3.669 0 Td (of )Tj -0.0091 Tc 1.161 0 Td (all )Tj 0.0353 Tc -35.951 -1.2 Td (possibilities )Tj 0.0197 Tc 5.583 0 Td (of )Tj 0.05 Tc 9.4056 0 0 9.3 78.57 128.89 Tm (distributing )Tj /T1_2 1 Tf -0.035 Tc 8.8654 0 0 16.9 130.45 128.89 Tm (rn )Tj /T1_0 1 Tf 0 Tc 16.9 0 0 16.9 140.74 128.89 Tm (-)Tj 9.3 0 0 9.3 149.62 128.89 Tm [(1 )50(-)]TJ /T1_1 1 Tf 0.05 Tc 6.9489 0 0 6.2 164.97 128.89 Tm (a1 )Tj /T1_2 1 Tf -0.028 Tc 10 0 0 10 174.94 128.89 Tm (\(t )Tj /T1_0 1 Tf 0 Tc 0.926 0 Td (-)Tj -0.035 Tc 9.1661 0 0 9.3 193.18 128.89 Tm (1\) )Tj 0.0348 Tc 9.3 0 0 9.3 204.03 128.89 Tm (ones )Tj 0.0422 Tc 2.343 0 Td (into )Tj /T1_2 1 Tf 0 Tc 10.3 0 0 10.3 245.04 128.89 Tm (t )Tj /T1_0 1 Tf 0.559 0 Td (-)Tj 9.3 0 0 9.3 259.78 128.89 Tm (1 )Tj 0.0409 Tc 0.81 0 Td (places )Tj 0.0268 Tc 3.067 0 Td (on )Tj 0 Tc 1.394 0 Td (a )Tj -0.0071 Tc 0.814 0 Td (line, )Tj 0.0148 Tc 2.137 0 Td (which )Tj 0.05 Tc 10.0686 0 0 9.3 15.92 117.18 Tm (can )Tj 0.0343 Tc 9.3 0 0 9.3 34.75 117.18 Tm (be )Tj 0.05 Tc 9.3585 0 0 9.3 47.43 117.18 Tm (computed )Tj -0.0033 Tc 9.3 0 0 9.3 91.45 117.18 Tm (by )Tj 0 Tc 10.1 0 0 10.1 96.85 85.5 Tm [(1 )32(-)]TJ /T1_1 1 Tf -0.035 Tc 3.3981 0 0 6 113.13 85.5 Tm (CL )Tj /T1_3 1 Tf 0 Tc 6.1 0 0 6.1 118.61 85.5 Tm (1 )Tj /T1_2 1 Tf -0.035 Tc 9.8127 0 0 10.3 122.92 85.5 Tm (\(t )Tj /T1_0 1 Tf 0 Tc 10.3 0 0 10.3 132.18 85.5 Tm (-)Tj -0.035 Tc 10.0137 0 0 10.1 141.49 85.5 Tm (1\)\) )Tj /T1_3 1 Tf 0 Tc 12.2 0 0 12.2 155.5 85.5 Tm (+ )Tj /T1_2 1 Tf -0.035 Tc 10.1193 0 0 10.3 165.4 85.5 Tm (\(t )Tj /T1_0 1 Tf 0 Tc 10.3 0 0 10.3 175.02 85.5 Tm (-)Tj -0.035 Tc 9.4138 0 0 10.1 184.71 85.5 Tm (1\) )Tj 0 Tc 10.1 0 0 10.1 195.54 85.5 Tm (-)Tj 0.05 Tc 13.5289 0 0 10.1 204.73 85.5 Tm (1\) )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 221.27 85.5 Tm (= )Tj 0.05 Tc 10.7098 0 0 8.1 234.04 85.5 Tm ("'"' )Tj /T1_2 1 Tf -0.035 Tc 10.9795 0 0 16.9 253.76 85.5 Tm (\(rn )Tj /T1_0 1 Tf 0 Tc 11.9 0 0 11.9 269.94 85.5 Tm (+ )Tj /T1_2 1 Tf 10.3 0 0 10.3 279.78 85.5 Tm (t )Tj /T1_0 1 Tf 0.594 0 Td (-)Tj 10.1 0 0 10.1 294.9 85.5 Tm [(3 )1(-)]TJ -0.035 Tc 3.849 0 0 10.1 311.25 85.5 Tm ({}, )Tj /T1_3 1 Tf 0 Tc 6.1 0 0 6.1 316.61 85.5 Tm (1 )Tj /T1_2 1 Tf -0.035 Tc 9.506 0 0 10 320.57 85.5 Tm (\(t )Tj /T1_0 1 Tf 0 Tc 10 0 0 10 329.64 85.5 Tm (-)Tj -0.035 Tc 9.4138 0 0 10.1 338.97 85.5 Tm (1\) )Tj 0 Tc 10.1 0 0 10.1 348.96 85.5 Tm (\) )Tj /T1_2 1 Tf -0.028 Tc 10 0 0 10 119.5 75.96 Tm (\(t )Tj /T1_0 1 Tf -0.0261 Tc 9.3 0 0 9.3 138.1 75.96 Tm (1\) )Tj 0 Tc 2.148 0 Td (1 )Tj /T1_1 1 Tf 9.5 0 0 9.5 234.07 75.96 Tm (L )Tj /T1_2 1 Tf 10.3 0 0 10.3 294 75.96 Tm (t )Tj /T1_0 1 Tf 0.594 0 Td (-)Tj 9.3 0 0 9.3 309.37 75.96 Tm [(2 )-4441(. )]TJ 0.05 Tc 9.9592 0 0 6.3001 231.92 69.31 Tm (al=l )Tj -0.035 Tc 9.6785 0 0 10.3 183.79 11.53 Tm (85 )Tj ET endstream endobj 147 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 45392/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream *P1 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553.33 Tm (\(3.4\), )Tj 0.0007 Tc 2.74 0 Td (we )Tj 0.0242 Tc 1.587 0 Td (have )Tj /T1_1 1 Tf 0 Tc 9.2 0 0 9.2 71.63 530.29 Tm (S )Tj /T1_0 1 Tf 11.4 0 0 11.4 80.58 530.29 Tm (= )Tj /T1_2 1 Tf 0.0045 Tc 10.4 0 0 10.4 91.05 530.29 Tm ({Igajl: )Tj /T1_3 1 Tf 0 Tc 8.9 0 0 8.9 122.53 530.29 Tm (j )Tj /T1_0 1 Tf 8.5 0 0 8.5 130.63 530.29 Tm (E )Tj /T1_1 1 Tf -0.035 Tc 6.7229 0 0 9.2 139.85 530.29 Tm ([0,11, )Tj /T1_3 1 Tf 0 Tc 9.2 0 0 9.2 159.04 530.29 Tm (-)Tj /T1_0 1 Tf -0.035 Tc 11.7959 0 0 20.8 168.77 530.29 Tm (2n )Tj 0 Tc 8.5 0 0 8.5 183.23 530.29 Tm (U )Tj /T1_2 1 Tf -0.0041 Tc 10.4 0 0 10.4 192.03 530.29 Tm ({Igajl: )Tj /T1_3 1 Tf 0 Tc 8.9 0 0 8.9 222.79 530.29 Tm (j )Tj /T1_0 1 Tf 8.5 0 0 8.5 230.53 530.29 Tm (E )Tj /T1_1 1 Tf -0.035 Tc 8.2395 0 0 9.2 239.39 530.29 Tm ([h )Tj 0.05 Tc 16.7644 0 0 9.2 249.43 530.29 Tm (-l,t )Tj /T1_0 1 Tf 12.5686 0 0 8.5 274.35 530.29 Tm (-I]} )Tj /T1_2 1 Tf 0 Tc 12.1 0 0 12.1 80.47 516.07 Tm (= )Tj -0.035 Tc 9.5929 0 0 10.4 91.25 516.07 Tm ({lgaj+h-11 )Tj /T1_0 1 Tf 0 Tc 10.4 0 0 10.4 135.46 516.07 Tm (: )Tj /T1_3 1 Tf 9 0 0 9 140.53 516.07 Tm (j )Tj /T1_0 1 Tf 8.8 0 0 8.8 148.09 516.07 Tm (E )Tj -0.035 Tc 9.6739 0 0 10.9 156.91 516.07 Tm ([t )Tj 0 Tc 10.9 0 0 10.9 165.83 516.07 Tm (-)Tj /T1_1 1 Tf 9.3 0 0 9.3 175.23 516.07 Tm (h )Tj /T1_3 1 Tf 12.3 0 0 12.3 182.86 516.07 Tm (+ )Tj /T1_0 1 Tf 0.0169 Tc 8.8 0 0 8.8 192.66 516.07 Tm (1, )Tj /T1_2 1 Tf 0 Tc 10.3 0 0 10.3 201.66 516.07 Tm (t )Tj /T1_0 1 Tf 0.577 0 Td (-)Tj 0.05 Tc 12.2309 0 0 8.8 216.99 516.07 Tm (In )Tj /T1_3 1 Tf 0 Tc 10.8 0 0 10.8 230.92 516.07 Tm (u )Tj /T1_2 1 Tf -0.035 Tc 9.5929 0 0 10.4 239.57 516.07 Tm ({lgaj+h-11 )Tj /T1_0 1 Tf 0 Tc 10.4 0 0 10.4 283.78 516.07 Tm (: )Tj /T1_3 1 Tf 9 0 0 9 288.67 516.07 Tm (j )Tj /T1_0 1 Tf 8.8 0 0 8.8 296.05 516.07 Tm (E )Tj -0.035 Tc 8.2856 0 0 8.8 305.08 516.07 Tm ([0, )Tj /T1_2 1 Tf 0 Tc 10.3 0 0 10.3 316.14 516.07 Tm (t )Tj /T1_1 1 Tf 0.05 Tc 10.4009 0 0 9.3 331.82 516.07 Tm (hn )Tj /T1_2 1 Tf 0 Tc 11.4 0 0 11.4 80.49 501.49 Tm (= )Tj -0.035 Tc 9.5495 0 0 10.4 91.43 501.49 Tm ({lgaj+h-11 )Tj /T1_0 1 Tf 0 Tc 10.4 0 0 10.4 135.46 501.49 Tm (: )Tj 9 0 0 9 140.61 501.49 Tm (j )Tj 8.8 0 0 8.8 148.09 501.49 Tm (E )Tj -0.035 Tc 9.3904 0 0 10.7 156.91 501.49 Tm ([0, )Tj /T1_2 1 Tf 0 Tc 9.8 0 0 9.8 168.9 501.49 Tm (t )Tj /T1_0 1 Tf 0.05 Tc 8.8219 0 0 8.8 184.8 501.49 Tm (I]}. )Tj 0.0379 Tc 9.3 0 0 9.3 35.77 477.55 Tm (Let )Tj /T1_1 1 Tf 0 Tc 11.5 0 0 11.5 52.95 477.55 Tm (f )Tj /T1_3 1 Tf 0.722 0 Td (: )Tj /T1_1 1 Tf 6.7 0 0 6.7 66.43 477.55 Tm (x )Tj /T1_3 1 Tf 6.8001 0 0 6.8001 74.72 477.55 Tm (H )Tj /T1_2 1 Tf 0.05 Tc 10.4461 0 0 10.4 86.67 477.55 Tm (g-a)Tj 0 Tc 4.9001 0 0 4.9001 102.58 479.89 Tm (h)Tj 0.88 -0.478 Td (-)Tj 1.018 0.514 Td (1)Tj /T1_1 1 Tf 6.7 0 0 6.7 115.75 477.55 Tm [(x)-433(, )]TJ /T1_0 1 Tf 0.05 Tc 9.6349 0 0 9.3 127.52 477.55 Tm (and )Tj 9.4215 0 0 9.3 146.25 477.55 Tm (denote )Tj /T1_1 1 Tf 10.3343 0 0 6.7 177.71 477.55 Tm (aj+h-l )Tj 10.1296 0 0 6.7 218.75 477.55 Tm (ah-l )Tj /T1_0 1 Tf 0 Tc 11.3 0 0 11.3 241.14 477.55 Tm (= )Tj /T1_2 1 Tf 10.4 0 0 10.4 251.2 477.55 Tm (b)Tj /T1_1 1 Tf 6.7 0 0 6.7 255.31 476.11 Tm (j)Tj 0.672 0.215 Td (. )Tj /T1_0 1 Tf 0.05 Tc 9.3191 0 0 9.3 266.37 477.55 Tm (We )Tj -0.0027 Tc 9.3 0 0 9.3 283.67 477.55 Tm (have: )Tj 0.0362 Tc -26.616 -5.052 Td (By )Tj 0.05 Tc 9.3399 0 0 9.3 52.15 430.57 Tm (Lemma )Tj 0.016 Tc 9.3 0 0 9.3 87.43 430.57 Tm (2.1, )Tj /T1_1 1 Tf -0.0065 Tc 9.6 0 0 9.6 107.19 430.57 Tm (Gp\(S\) )Tj /T1_0 1 Tf -0.0305 Tc 9.3 0 0 9.3 138.16 430.57 Tm (is )Tj 0.042 Tc 1.181 0 Td (isomorphic )Tj 0.0383 Tc 5.406 0 Td (to )Tj /T1_1 1 Tf -0.006 Tc 9.6 0 0 9.6 211.95 430.57 Tm (Gp\(S*\). )Tj /T1_0 1 Tf -0.014 Tc 9.3 0 0 9.3 252.58 430.57 Tm (Now )Tj -0.035 Tc 9.1156 0 0 9.3 276.11 430.57 Tm (we )Tj 0.0039 Tc 9.3 0 0 9.3 291.4 430.57 Tm (verify )Tj 0.05 Tc 10.5068 0 0 9.3 318.93 430.57 Tm (that )Tj /T1_1 1 Tf -0.035 Tc 9.4987 0 0 9.6 341.86 430.57 Tm ({b)Tj 0 Tc 6.2 0 0 6.2 350.87 429.13 Tm (j )Tj /T1_3 1 Tf 1.534 0.232 Td (: )Tj /T1_0 1 Tf 9 0 0 9 367.05 430.57 Tm (j )Tj 8.1 0 0 8.1 376.7 430.57 Tm (E )Tj /T1_1 1 Tf -0.035 Tc 7.8907 0 0 10.5 36.71 418.87 Tm ([0, )Tj /T1_2 1 Tf 0 Tc 10.3 0 0 10.3 47.76 418.87 Tm (t )Tj /T1_0 1 Tf 0.594 0 Td (-)Tj 0.0155 Tc 9.3 0 0 9.3 63.3 418.87 Tm (I]} )Tj 0.0293 Tc 1.58 0 Td (satisfies )Tj 0.0241 Tc 3.912 0 Td (\(3.2\) )Tj 0.05 Tc 9.5174 0 0 9.3 137.42 418.87 Tm (and )Tj 0.0312 Tc 9.3 0 0 9.3 156.31 418.87 Tm (\(3.3\). )Tj 0.05 Tc 9.3177 0 0 9.3 183.2 418.87 Tm (From )Tj 0.0167 Tc 9.3 0 0 9.3 208.87 418.87 Tm (\(3.5-7\), )Tj -0.035 Tc 9.2755 0 0 9.3 241.55 418.87 Tm (we )Tj 0.0312 Tc 9.3 0 0 9.3 255.77 418.87 Tm (have: )Tj -0.0245 Tc -23.596 -5.11 Td (We )Tj 0.0028 Tc 1.852 0 Td (also )Tj 0.0178 Tc 2.118 0 Td (have )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 95.87 371.35 Tm (b)Tj 7.1 0 0 7.1 100.18 370.27 Tm (t)Tj 0.486 0.152 Td (-)Tj /T1_1 1 Tf 6 0 0 6 109.36 370.27 Tm (1 )Tj /T1_3 1 Tf 10.8 0 0 10.8 117.73 371.35 Tm (< )Tj /T1_1 1 Tf 0.05 Tc 6.6822 0 0 6 128.64 371.35 Tm (Tn, )Tj /T1_0 1 Tf 0.0256 Tc 9.3 0 0 9.3 144.05 371.35 Tm (since )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 168.59 371.35 Tm (b)Tj /T1_1 1 Tf 5.6 0 0 5.6 172.71 370.45 Tm (t)Tj 0.614 0.161 Td (-)Tj 6 0 0 6 182.08 370.45 Tm (1 )Tj /T1_0 1 Tf 11.3 0 0 11.3 190.02 371.35 Tm (= )Tj /T1_1 1 Tf 0.05 Tc 8.858 0 0 6.7 200.95 371.35 Tm (at+h-2 )Tj /T1_3 1 Tf 0 Tc 6.7 0 0 6.7 232.68 371.35 Tm (-)Tj /T1_1 1 Tf 0.05 Tc 10.4305 0 0 6.7 241.79 371.35 Tm (ah-l )Tj /T1_0 1 Tf 0 Tc 12.1 0 0 12.1 265.98 371.35 Tm (= )Tj /T1_2 1 Tf 0.05 Tc 6.9566 0 0 6.5001 277.42 371.35 Tm (Tn )Tj /T1_1 1 Tf 9.8236 0 0 6.7 298.56 371.35 Tm (\(ah-l )Tj /T1_3 1 Tf 0 Tc 6.7 0 0 6.7 324.84 371.35 Tm (-)Tj /T1_1 1 Tf 0.05 Tc 9.2446 0 0 6.7 334.68 371.35 Tm (ah-2\) )Tj /T1_3 1 Tf 0 Tc 10.8 0 0 10.8 363.61 371.35 Tm (< )Tj /T1_1 1 Tf 0.05 Tc 6.9597 0 0 6 374.34 371.35 Tm (nl, )Tj /T1_0 1 Tf 0.0061 Tc 9.3 0 0 9.3 36.64 360.19 Tm (if )Tj 0 Tc 1.048 0 Td (2 )Tj -0.035 Tc 5.8592 0 0 9.3 56.19 360.19 Tm (:::; )Tj /T1_2 1 Tf 0 Tc 9.1 0 0 9.1 68.17 360.19 Tm (h )Tj /T1_0 1 Tf -0.035 Tc 5.6702 0 0 9.1 78.52 360.19 Tm (:::; )Tj /T1_2 1 Tf 0.0011 Tc 10 0 0 10 90.24 360.19 Tm (t, )Tj /T1_0 1 Tf 0.05 Tc 9.6349 0 0 9.3 101.42 360.19 Tm (and )Tj /T1_2 1 Tf 0 Tc 9.1 0 0 9.1 121.79 360.19 Tm (b)Tj 7.1 0 0 7.1 126.1 358.93 Tm (t)Tj 0.461 0.177 Td (-)Tj /T1_1 1 Tf 6.1 0 0 6.1 135.45 358.93 Tm (1 )Tj /T1_0 1 Tf 12.1 0 0 12.1 144.3 360.19 Tm (= )Tj /T1_1 1 Tf 0.05 Tc 11.4003 0 0 6.1 156.09 360.19 Tm (at-l )Tj /T1_3 1 Tf 0 Tc 6.1 0 0 6.1 178.51 360.19 Tm (-)Tj /T1_1 1 Tf 0.05 Tc 7.2648 0 0 6.1 188.55 360.19 Tm (ao )Tj /T1_0 1 Tf 0 Tc 11.2 0 0 11.2 203.16 360.19 Tm (< )Tj /T1_1 1 Tf 0.05 Tc 11.1628 0 0 6.1 214.6 360.19 Tm (at-l )Tj /T1_0 1 Tf -0.035 Tc 6.5666 0 0 13.3 237.98 360.19 Tm (:s: )Tj /T1_2 1 Tf 0.05 Tc 6.9566 0 0 6.5001 249.52 360.19 Tm (Tn )Tj /T1_0 1 Tf 0.0061 Tc 9.3 0 0 9.3 262.9 360.19 Tm (if )Tj /T1_2 1 Tf 0 Tc 9.1 0 0 9.1 273.19 360.19 Tm (h )Tj /T1_0 1 Tf 12.1 0 0 12.1 283.98 360.19 Tm (= )Tj -0.035 Tc 8.9497 0 0 9.1 295.97 360.19 Tm (1. )Tj 0.0436 Tc 9.3 0 0 9.3 310.82 360.19 Tm (Finally, )Tj 0.0007 Tc 3.99 0 Td (we )Tj 0.0307 Tc 1.723 0 Td (have )Tj /T1_2 1 Tf 0.05 Tc 9.3106 0 0 6.5001 36.53 348.67 Tm (Tn> )Tj /T1_1 1 Tf 0 Tc 9.1 0 0 9.1 57.69 348.67 Tm (b)Tj /T1_2 1 Tf 7.3001 0 0 7.3001 61.84 347.23 Tm (t)Tj 0.448 0.197 Td (-)Tj 6.4001 0 0 6.4001 70.99 347.23 Tm (1 )Tj /T1_0 1 Tf 12.1 0 0 12.1 77.7 348.67 Tm (= )Tj /T1_1 1 Tf -0.035 Tc 8.2318 0 0 9.1 88 348.67 Tm (\(b)Tj /T1_2 1 Tf 0 Tc 7.6 0 0 7.6 95.67 347.23 Tm (t)Tj 0.454 0.189 Td (-)Tj 6.4001 0 0 6.4001 105.37 347.41 Tm (1 )Tj /T1_0 1 Tf 0.991 0.197 Td (-)Tj /T1_1 1 Tf 9.1 0 0 9.1 121.05 348.67 Tm (b)Tj /T1_2 1 Tf 7.3001 0 0 7.3001 125.38 347.41 Tm (t)Tj 0.448 0.173 Td (-)Tj 6.4001 0 0 6.4001 134.62 347.41 Tm (2)Tj 0.739 0.197 Td (\) )Tj /T1_3 1 Tf 12.3 0 0 12.3 144.7 348.67 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 8.4429 0 0 9.1 154.41 348.67 Tm (\(b)Tj /T1_2 1 Tf 0 Tc 7.3001 0 0 7.3001 162.28 347.41 Tm (t)Tj 0.497 0.173 Td (-)Tj 6.4001 0 0 6.4001 171.52 347.41 Tm (2 )Tj /T1_0 1 Tf 1.089 0.197 Td (-)Tj /T1_1 1 Tf 9.1 0 0 9.1 187.65 348.67 Tm (b)Tj /T1_2 1 Tf 7.3001 0 0 7.3001 191.8 347.41 Tm (t)Tj 0.473 0.173 Td (-)Tj 6.4001 0 0 6.4001 200.82 347.41 Tm (3)Tj 0.717 0.197 Td (\) )Tj /T1_3 1 Tf 12.3 0 0 12.3 210.94 348.67 Tm (+ )Tj -0.035 Tc 8.9027 0 0 12.3 220.8 348.67 Tm (... )Tj 0 Tc 12.3 0 0 12.3 230.74 348.67 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 8.7794 0 0 10 240.38 348.67 Tm (\(b)Tj 0 Tc 6.2 0 0 6.2 248.19 347.59 Tm (1 )Tj /T1_1 1 Tf 9.1 0 0 9.1 264.15 348.67 Tm (b)Tj /T1_2 1 Tf 10 0 0 10 268.12 347.41 Tm (o)Tj 0.509 0.126 Td (\) )Tj /C0_0 1 Tf 5.5801 0 0 7.5601 280.27 348.67 Tm <007E0020>Tj /T1_2 1 Tf 0.0112 Tc 10 0 0 10 289.71 348.67 Tm (e\(t )Tj /T1_0 1 Tf -0.0261 Tc 9.3 0 0 9.3 312.88 348.67 Tm (1\) )Tj 0.05 Tc 9.3496 0 0 9.3 324.53 348.67 Tm (which )Tj 0.0353 Tc 9.3 0 0 9.3 353.26 348.67 Tm (implies )Tj 0.05 Tc 9.9596 0 0 9.3 36.88 337.33 Tm (that )Tj 0 Tc 9.3 0 0 9.3 57.14 337.33 Tm (e )Tj 11.4 0 0 11.4 64.38 337.33 Tm (= )Tj /T1_2 1 Tf 9.4 0 0 9.4 74.45 337.33 Tm (b)Tj /T1_1 1 Tf 6.2 0 0 6.2 78.57 335.71 Tm (1 )Tj /T1_3 1 Tf 10.8 0 0 10.8 85.51 337.33 Tm (< )Tj /T1_2 1 Tf 0.05 Tc 6.9566 0 0 6.5001 95.44 337.33 Tm (Tn )Tj /T1_0 1 Tf 0 Tc 6.5001 0 0 6.5001 104.22 337.33 Tm (/ )Tj 0.05 Tc 9.2654 0 0 8.8 109.33 337.33 Tm (\(t )Tj 0 Tc 8.8 0 0 8.8 118.7 337.33 Tm (-)Tj 0.0168 Tc 9.3 0 0 9.3 128.74 337.33 Tm (1\), )Tj 0.05 Tc 9.5174 0 0 9.3 142.82 337.33 Tm (and )Tj 9.5056 0 0 9.3 161.62 337.33 Tm (this )Tj 0.0095 Tc 9.3 0 0 9.3 180.62 337.33 Tm (finishes )Tj 0.05 Tc 9.5625 0 0 9.3 214.36 337.33 Tm (the )Tj 0.0141 Tc 9.3 0 0 9.3 230.95 337.33 Tm (proof. )Tj /T1_4 1 Tf 0.0121 Tc 9.7 0 0 9.7 37.01 309.07 Tm (4. )Tj 0.05 Tc 10.3458 0 0 9.7 50.38 309.07 Tm (An )Tj 10.2001 0 0 9.7 68.02 309.07 Tm (Algorithm )Tj /T1_0 1 Tf -0.0051 Tc 9.3 0 0 9.3 55.59 292.15 Tm (We )Tj 0.0136 Tc 1.697 0 Td (define )Tj 0.05 Tc 9.5625 0 0 9.3 98.62 292.15 Tm (the )Tj /T1_2 1 Tf 0.029 Tc 9.1 0 0 9.1 115.31 292.15 Tm (clique )Tj 0.05 Tc 9.4169 0 0 9.1 142.33 292.15 Tm (number )Tj /T1_0 1 Tf 9.6349 0 0 9.3 175.58 292.15 Tm (and )Tj 9.5625 0 0 9.3 193.66 292.15 Tm (the )Tj /T1_2 1 Tf 0.0417 Tc 9.1 0 0 9.1 209.95 292.15 Tm (independence )Tj 0.05 Tc 9.4169 0 0 9.1 267.61 292.15 Tm (number )Tj /T1_0 1 Tf 0.039 Tc 9.3 0 0 9.3 300.69 292.15 Tm (of )Tj 0 Tc 1.084 0 Td (a )Tj 0.05 Tc 9.8729 0 0 9.3 317.98 292.15 Tm (graph )Tj 10.0407 0 0 9.3 345.58 292.15 Tm (to )Tj 9.5181 0 0 9.3 357.31 292.15 Tm (be )Tj 9.4259 0 0 9.3 370.06 292.15 Tm (the )Tj 0.0363 Tc 9.3 0 0 9.3 37 280.81 Tm (largest )Tj 0.0391 Tc 3.289 0 Td (order )Tj 0.05 Tc 9.3902 0 0 9.3 92.61 280.81 Tm (of )Tj 0.0485 Tc 9.3 0 0 9.3 103.95 280.81 Tm (any )Tj 0.0308 Tc 1.974 0 Td (clique )Tj 0.05 Tc 9.8699 0 0 9.3 150.2 280.81 Tm (and )Tj 9.6991 0 0 9.3 169.54 280.81 Tm (the )Tj 0.0395 Tc 9.3 0 0 9.3 186.22 280.81 Tm (largest )Tj 0.044 Tc 3.328 0 Td (order )Tj 0.039 Tc 2.671 0 Td (of )Tj 0.0485 Tc (any )Tj 0.05 Tc 9.3575 0 0 9.3 271.72 280.81 Tm (independent )Tj 9.7318 0 0 9.3 326.2 280.81 Tm (set )Tj 9.4583 0 0 9.3 341.91 280.81 Tm (contained )Tj -0.006 Tc 9.3 0 0 9.3 37.18 269.29 Tm (in )Tj 0.05 Tc 9.5625 0 0 9.3 48.58 269.29 Tm (the )Tj 0.0474 Tc 9.3 0 0 9.3 65.62 269.29 Tm (graph, )Tj 0.0319 Tc 3.298 0 Td (respectively. )Tj 0.05 Tc 9.3191 0 0 9.3 154.41 269.29 Tm (We )Tj 0.0338 Tc 9.3 0 0 9.3 172.06 269.29 Tm (know )Tj 0.05 Tc 10.0691 0 0 9.3 198.34 269.29 Tm (that )Tj 0 Tc 9.3 0 0 9.3 219.69 269.29 Tm (a )Tj 0.0035 Tc 0.929 0 Td (cyclic )Tj 0.05 Tc 9.7998 0 0 9.3 255.16 269.29 Tm (graph )Tj -0.035 Tc 9.0754 0 0 9.3 283.79 269.29 Tm (is )Tj 0.05 Tc 9.3541 0 0 9.3 294.1 269.29 Tm (vertex-transitive. )Tj -0.015 Tc 9.3 0 0 9.3 373.15 269.29 Tm (So )Tj 0.05 Tc 9.4259 0 0 9.3 37.24 257.77 Tm (the )Tj 0.0192 Tc 9.3 0 0 9.3 53.55 257.77 Tm (clique )Tj 0.05 Tc 9.5464 0 0 9.3 80.81 257.77 Tm (number )Tj 9.8076 0 0 9.3 116.19 257.77 Tm (of )Tj /T1_1 1 Tf -0.0159 Tc 9.6 0 0 9.6 127.71 257.77 Tm (Gp\(S\) )Tj /T1_0 1 Tf 0.0082 Tc 9.3 0 0 9.3 157.42 257.77 Tm (is )Tj 0.0497 Tc 1.101 0 Td (equal )Tj 0.05 Tc 9.6041 0 0 9.3 193.48 257.77 Tm (to )Tj 9.4259 0 0 9.3 205.54 257.77 Tm (the )Tj 9.3574 0 0 9.3 222.28 257.77 Tm (maximal )Tj 9.5954 0 0 9.3 261.27 257.77 Tm (order )Tj 9.3902 0 0 9.3 287.19 257.77 Tm (of )Tj 0.0292 Tc 9.3 0 0 9.3 298.35 257.77 Tm (any )Tj 0.0425 Tc 1.935 0 Td (clique )Tj 0.05 Tc 9.7676 0 0 9.3 344.98 257.77 Tm (in )Tj /T1_1 1 Tf -0.0065 Tc 9.6 0 0 9.6 356.85 257.77 Tm (Gp\(S\) )Tj /T1_0 1 Tf 0.0369 Tc 9.3 0 0 9.3 37.17 246.25 Tm (containing )Tj -0.035 Tc 7.0839 0 0 9.3 82.91 246.25 Tm (O. )Tj 0.0171 Tc 9.3 0 0 9.3 95 246.25 Tm (Define )Tj /T1_1 1 Tf 0.05 Tc 12.7271 0 0 10 66.14 222.85 Tm (A={x:lxIES}, )Tj /C0_0 1 Tf 0 Tc 7.1724 0 0 8.64 152.47 222.85 Tm <0053003D007B00780045005A003A003A0058007E0053007D002C0020>Tj /T1_1 1 Tf 0.05 Tc 12.6655 0 0 10 258.2 222.85 Tm (A={x:lxIES}. )Tj -0.035 Tc 9.4995 0 0 9.6 363.9 222.85 Tm (\(4.1\) )Tj /T1_0 1 Tf 0.0418 Tc 9.3 0 0 9.3 37.4 199.81 Tm (Denote )Tj 0.0492 Tc 3.544 0 Td (the )Tj 0.0497 Tc 1.794 0 Td (induced )Tj 0.05 Tc 9.5089 0 0 9.3 123.71 199.81 Tm (sub-graph )Tj 9.3236 0 0 9.3 169.66 199.81 Tm (in )Tj /T1_1 1 Tf -0.0206 Tc 9.6 0 0 9.6 181.35 199.81 Tm (Gp\(S\) )Tj /T1_0 1 Tf 0.0158 Tc 9.3 0 0 9.3 210.77 199.81 Tm (whose )Tj 0.05 Tc 9.3268 0 0 9.3 239.38 199.81 Tm (vertex )Tj 9.8839 0 0 9.3 268.78 199.81 Tm (set )Tj -0.035 Tc 9.0754 0 0 9.3 285.05 199.81 Tm (is )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 295.08 199.81 Tm (A )Tj /T1_0 1 Tf -0.0227 Tc 9.3 0 0 9.3 305.83 199.81 Tm (by )Tj /T1_1 1 Tf 0.003 Tc 9.6 0 0 9.6 319.05 199.81 Tm (Gp[A]. )Tj /T1_0 1 Tf 0.05 Tc 9.4086 0 0 9.3 353.48 199.81 Tm (Denote )Tj 9.4259 0 0 9.3 37.6 188.11 Tm (the )Tj 0.0154 Tc 9.3 0 0 9.3 53.91 188.11 Tm (clique )Tj 0.05 Tc 9.4918 0 0 9.3 80.99 188.11 Tm (number )Tj 9.8076 0 0 9.3 116.37 188.11 Tm (of )Tj /T1_1 1 Tf -0.0206 Tc 9.6 0 0 9.6 127.89 188.11 Tm (Gp\(S\) )Tj /T1_0 1 Tf 0.05 Tc 9.8699 0 0 9.3 157.4 188.11 Tm (and )Tj /T1_1 1 Tf -0.0207 Tc 9.6 0 0 9.6 176.67 188.11 Tm (Gp[A] )Tj /T1_0 1 Tf 0.0354 Tc 9.3 0 0 9.3 204.67 188.11 Tm (by )Tj /T1_1 1 Tf -0.035 Tc 9.5885 0 0 9.6 218.87 188.11 Tm ([Gp\(S\)] )Tj /T1_0 1 Tf 0.05 Tc 9.7524 0 0 9.3 252.44 188.11 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 8.6331 0 0 9.6 272.15 188.11 Tm ([AJ, )Tj /T1_0 1 Tf 0.0271 Tc 9.3 0 0 9.3 290.69 188.11 Tm (respectively. )Tj 0.0336 Tc 6.075 0 Td (We )Tj 0.0307 Tc 1.86 0 Td (have )Tj /T1_1 1 Tf -0.035 Tc 9.5293 0 0 9.6 38.15 176.59 Tm ([Gp\(S\)] )Tj /T1_0 1 Tf 0 Tc 12.1 0 0 12.1 71.04 176.59 Tm (= )Tj /T1_1 1 Tf -0.011 Tc 9.6 0 0 9.6 81.17 176.59 Tm ([AJ+ )Tj /T1_3 1 Tf -0.035 Tc 8.1087 0 0 8.5 102.52 176.59 Tm (1. )Tj /T1_0 1 Tf 0.05 Tc 10.0089 0 0 9.3 111.87 176.59 Tm (The )Tj 9.6677 0 0 9.3 131.31 176.59 Tm (computation )Tj -0.0305 Tc 9.3 0 0 9.3 187.3 176.59 Tm (is )Tj 0.0292 Tc 0.974 0 Td (much )Tj 0.0261 Tc 2.624 0 Td (easier )Tj 0.0255 Tc 2.77 0 Td (if )Tj -0.0186 Tc 0.84 0 Td (we )Tj 0.0408 Tc 1.472 0 Td (use )Tj /T1_1 1 Tf -0.0301 Tc 9.6 0 0 9.6 284.13 176.59 Tm (Gp[A] )Tj /T1_0 1 Tf 0.0414 Tc 9.3 0 0 9.3 310.6 176.59 Tm (iIlstead )Tj 0.05 Tc 10.0163 0 0 9.3 343.7 176.59 Tm (of )Tj /T1_1 1 Tf -0.0044 Tc 9.6 0 0 9.6 354.51 176.59 Tm (Gp\(S\). )Tj /T1_0 1 Tf 0.05 Tc 9.459 0 0 9.3 37.72 165.25 Tm (The )Tj 0.0389 Tc 9.3 0 0 9.3 56.44 165.25 Tm (independence )Tj 0.05 Tc 9.5464 0 0 9.3 115.37 165.25 Tm (number )Tj 9.3902 0 0 9.3 150.21 165.25 Tm (of )Tj /T1_1 1 Tf -0.0018 Tc 9.6 0 0 9.6 160.83 165.25 Tm (Gp\(S\) )Tj /T1_0 1 Tf -0.0111 Tc 9.3 0 0 9.3 190.18 165.25 Tm (is )Tj 0.0448 Tc 0.985 0 Td (equal )Tj 0.05 Tc 9.3858 0 0 9.3 224.44 165.25 Tm (to )Tj 9.4259 0 0 9.3 235.42 165.25 Tm (the )Tj 0.0347 Tc 9.3 0 0 9.3 251.37 165.25 Tm (clique )Tj 0.0443 Tc 3.009 0 Td (number )Tj 0.05 Tc 9.3902 0 0 9.3 313.11 165.25 Tm (of )Tj /T1_1 1 Tf 0.0069 Tc 9.6 0 0 9.6 323.91 165.25 Tm (Gp\(S\). )Tj /T1_0 1 Tf 0.0328 Tc 9.3 0 0 9.3 357.98 165.25 Tm (Hence )Tj /T1_1 1 Tf 0.016 Tc 9.9 0 0 9.9 152.33 141.85 Tm (R\([A] )Tj /T1_3 1 Tf 0 Tc 12.3 0 0 12.3 178.9 141.85 Tm (+ )Tj /T1_0 1 Tf 0.0137 Tc 8.7 0 0 8.7 188.59 141.85 Tm (2, )Tj /T1_1 1 Tf -0.035 Tc 8.9837 0 0 10.5 198.17 141.85 Tm ([A] )Tj /T1_3 1 Tf 0 Tc 12.3 0 0 12.3 212.2 141.85 Tm (+ )Tj /T1_0 1 Tf -0.0072 Tc 8.7 0 0 8.7 221.89 141.85 Tm (2\) )Tj /C0_0 1 Tf 0 Tc 5.5801 0 0 8.8201 233.29 141.85 Tm <007E0020>Tj /T1_1 1 Tf 8.1 0 0 8.1 242.13 141.85 Tm (p )Tj /T1_3 1 Tf 12.3 0 0 12.3 249.64 141.85 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 8.9497 0 0 9.1 259.61 141.85 Tm (1. )Tj 0 Tc 9.3 0 0 9.3 361.33 142.39 Tm (\( )Tj 0.0246 Tc 0.375 0 Td (4.2\). )Tj -0.014 Tc -33.127 -2.535 Td (Now )Tj -0.035 Tc 9.1156 0 0 9.3 78.29 118.81 Tm (we )Tj 0.0058 Tc 9.3 0 0 9.3 92.62 118.81 Tm (give )Tj 0.05 Tc 10.0821 0 0 9.3 112.76 118.81 Tm (an )Tj 9.5204 0 0 9.3 126.8 118.81 Tm (algorithm )Tj 0.0074 Tc 9.3 0 0 9.3 171.26 118.81 Tm (for )Tj 0.0189 Tc 1.645 0 Td (finding )Tj -0.0085 Tc 3.467 0 Td (lower )Tj 0.05 Tc 9.3953 0 0 9.3 243.91 118.81 Tm (bounds, )Tj 0.0433 Tc 9.3 0 0 9.3 280.81 118.81 Tm (based )Tj 0.0075 Tc 2.873 0 Td (on )Tj 0.0312 Tc 1.508 0 Td (\(4.2\). )Tj -0.0146 Tc 3.012 0 Td (\\Ve )Tj 0.0139 Tc 1.867 0 Td (first )Tj 0.0111 Tc -35.352 -1.258 Td (need )Tj 0.05 Tc 9.3858 0 0 9.3 59.74 107.11 Tm (to )Tj -0.0039 Tc 9.3 0 0 9.3 71.01 107.11 Tm (do )Tj 0.0474 Tc 1.351 0 Td (some )Tj 0.05 Tc 9.6072 0 0 9.3 108.01 107.11 Tm (preparation )Tj 0.0171 Tc 9.3 0 0 9.3 160.1 107.11 Tm (for )Tj 0.0441 Tc 1.598 0 Td (using )Tj 0.05 Tc 9.4259 0 0 9.3 200.14 107.11 Tm (the )Tj 0.043 Tc 9.3 0 0 9.3 216.45 107.11 Tm (algorithm. )Tj 0.05 Tc 9.4167 0 0 9.3 263.66 107.11 Tm (For )Tj 0.0196 Tc 9.3 0 0 9.3 281.08 107.11 Tm (given )Tj /T1_2 1 Tf -0.035 Tc 7.1975 0 0 9.3 305.96 107.11 Tm (q2 )Tj /C0_0 1 Tf 0 Tc 5.7601 0 0 7.0201 317.53 107.11 Tm <007E0020>Tj /T1_0 1 Tf 0.05 Tc 8.8149 0 0 8.8 327.52 107.11 Tm (ql )Tj /C0_0 1 Tf 0 Tc 5.7601 0 0 7.0201 339.67 107.11 Tm <007E0020>Tj /T1_0 1 Tf 0.0224 Tc 9.3 0 0 9.3 349.45 107.11 Tm (3, )Tj 0.0345 Tc 1.159 0 Td (select )Tj 0 Tc -34.641 -1.22 Td (a )Tj 0.0488 Tc 0.901 0 Td (prime )Tj /T1_1 1 Tf 0 Tc 8.3 0 0 8.3 73.65 95.76 Tm (p )Tj /T1_3 1 Tf 8.1 0 0 8.1 82.49 95.76 Tm (= )Tj /T1_0 1 Tf 0.05 Tc 9.3571 0 0 9.3 94.26 95.76 Tm (2m )Tj /T1_3 1 Tf 0 Tc 12.3 0 0 12.3 109.96 95.76 Tm (+ )Tj /T1_0 1 Tf 9.3 0 0 9.3 120.46 95.76 Tm (1 )Tj 0.05 Tc 9.6349 0 0 9.3 129.32 95.76 Tm (and )Tj 0.0182 Tc 9.3 0 0 9.3 148.58 95.76 Tm (find )Tj 0 Tc 2.208 0 Td (a )Tj 0.0467 Tc 0.959 0 Td (primitive )Tj 0.05 Tc 9.4108 0 0 9.3 219.77 95.76 Tm (root )Tj /T1_1 1 Tf 0 Tc 8.3 0 0 8.3 240.42 95.76 Tm (g )Tj /T1_0 1 Tf 0.05 Tc 9.4923 0 0 9.3 249.64 95.76 Tm (modulo )Tj /T1_1 1 Tf -0.0059 Tc 8.3 0 0 8.3 284.79 95.76 Tm (p. )Tj /T1_0 1 Tf 0.0205 Tc 9.3 0 0 9.3 299.3 95.76 Tm (For )Tj 0.05 Tc 9.8357 0 0 9.3 317.14 95.76 Tm (the )Tj 0.0475 Tc 9.3 0 0 9.3 334.67 95.76 Tm (selected )Tj /T1_2 1 Tf 0.05 Tc 9.0752 0 0 7.6 372.55 95.76 Tm (nt, )Tj /T1_0 1 Tf 0.0152 Tc 9.3 0 0 9.3 38.03 84.07 Tm (select )Tj 0 Tc 2.772 0 Td (a )Tj 0.0361 Tc 0.824 0 Td (positive )Tj 0.047 Tc 3.823 0 Td (integer )Tj /T1_2 1 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obj <> endobj 132 0 obj <> endobj 133 0 obj <> endobj 134 0 obj <> endobj 135 0 obj <> endobj 136 0 obj <> endobj 196 0 obj <>stream Hd͊zy8 >sRhF^#y QG#Oç==o/ϧ;c_mӷKv|~_oo~y>}~W=|z>{O݇q~?>Ï?o+~ߒ~;%zΏx߽w;>lp?(O?{wٸ^ PZUuTGu^5P5FjFDMԤU PjVjUmFmک]uPuNNE]E5|| _#_k55|| _#_k55|| _#_k55|| _#_k5Z||-_+_kZ||-_+_kZ||-_+_kZ||-_+_ku:||_'_uu:||_'_uu:||_'_uu:||_'_uz||=_/_z||=_/_z||=_/_z||=_/_ || ߀o77 || ߀o77 || ߀o77 || ߀o77 KG#(~? ?G#(~? ?G#(~? ?G#(~? ?z $߄o77MM&|| $߄o77MM&|| $߄o77MM&|| $߄o77MM&||3,ߌo77f||3,ߌo77f||3,ߌo77f||3,ߌo77f|| "߂oȷ[--|| "߂oȷ[--|| "߂oȷ[--|| "߂oȷ[--||+*ߊoŷʷ[V||+*ߊoŷʷ[V||+*ߊoŷʷ[V||+*ߊoŷʷ[V|| &߆o÷ɷmm6|| &߆o÷ɷmm6|| &߆o÷ɷmm6|| &߆o÷ɷmm6|ۯ\t;]~~߅ww;]~~߅ww;]~~߅ww;]~~߅w߁w;;|C߁w;;|C߁w;;|C߁w;;|C߉w;;NN|'S߉w;;NN|'S߉w;;NN|'S߉w;;NN|'S ߅w]..|K ߅w]..|K ߅w]..|K ߅w]..|?|x>stream q 403.1999969 0 0 336.9600067 0 239.0399933 cm /Im0 Do Q q 403.1999969 0 0 239.0399933 0 0 cm /Im1 Do Q BT /T1_0 1 Tf 0.05 Tc 3 Tr 11.1189 0 0 9.5 12.18 546.49 Tm (Lemma )Tj 9.932 0 0 9.5 53.4 546.49 Tm (2.1. )Tj /T1_1 1 Tf 0.0465 Tc 9.6 0 0 9.6 76.78 546.49 Tm (Let )Tj 0 Tc 1.798 0 Td (g )Tj /T1_0 1 Tf -0.005 Tc 9.5 0 0 9.5 103.69 546.49 Tm (be )Tj 0 Tc 1.353 0 Td (a )Tj /T1_1 1 Tf 0.0384 Tc 9.6 0 0 9.6 124.88 546.49 Tm (primitive )Tj 0.0451 Tc 4.293 0 Td (root )Tj 0.05 Tc 9.7475 0 0 9.6 188.06 546.49 Tm (modulo )Tj -0.0251 Tc 9.6 0 0 9.6 223.34 546.49 Tm (p. )Tj -0.0213 Tc 1.494 0 Td (For )Tj 0.05 Tc 9.6208 0 0 9.6 255.54 546.49 Tm (any )Tj 9.7353 0 0 9.3 274.65 546.49 Tm (j, )Tj 0 Tc 9.6 0 0 9.6 283.07 546.49 Tm (b )Tj /T1_0 1 Tf 7.7 0 0 7.7 291.2 546.49 Tm (E )Tj /T1_2 1 Tf 0.05 Tc 7.4313 0 0 6 301.27 546.49 Tm (ZPl )Tj /T1_1 1 Tf 0.0212 Tc 9.6 0 0 9.6 318.31 546.49 Tm (the )Tj -0.0001 Tc 1.706 0 Td (linear )Tj 0.044 Tc -33.525 -1.219 Td (transformation )Tj /T1_2 1 Tf 0 Tc 11.6 0 0 11.6 80.49 534.79 Tm (f )Tj /T1_3 1 Tf 0.84 0 Td (: )Tj /T1_2 1 Tf 8.1 0 0 8.1 96.67 534.79 Tm (x )Tj /T1_3 1 Tf 6.8001 0 0 6.8001 106.04 534.79 Tm (H )Tj /T1_2 1 Tf 0.05 Tc 9.7017 0 0 8.1 119.27 534.79 Tm (gjx )Tj /T1_3 1 Tf 0 Tc 12.2 0 0 12.2 136.42 534.79 Tm (+ )Tj /T1_1 1 Tf 9.6 0 0 9.6 146.45 534.79 Tm (b )Tj -0.0303 Tc 0.82 0 Td (is )Tj -0.0162 Tc 1.094 0 Td (an )Tj 0.0439 Tc 1.494 0 Td (isomorphism )Tj /T1_2 1 Tf 0 Tc 11.6 0 0 11.6 237.45 534.79 Tm (f )Tj /T1_3 1 Tf 0.855 0 Td (: )Tj /T1_2 1 Tf -0.0065 Tc 9.6 0 0 9.6 253.71 534.79 Tm (Gp\(S\) )Tj /T1_0 1 Tf 0.05 Tc 13.0189 0 0 8.4 284.43 534.79 Tm (-t )Tj /T1_2 1 Tf -0.0153 Tc 9.6 0 0 9.6 297.63 534.79 Tm (Gp\(S*\), )Tj /T1_1 1 Tf 0.0008 Tc 3.811 0 Td (where )Tj /T1_2 1 Tf 0.0148 Tc -33.542 -1.237 Td (S* )Tj /T1_0 1 Tf 0 Tc 11.3 0 0 11.3 26.76 522.91 Tm (= )Tj /T1_2 1 Tf 0.05 Tc 9.6901 0 0 8.1 37.47 522.91 Tm ({Igjxl )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 64.77 522.91 Tm (: )Tj /T1_2 1 Tf 0.05 Tc 10.617 0 0 9.2 70.13 522.91 Tm (XES}. )Tj /T1_1 1 Tf 9.7049 0 0 9.6 13.03 500.59 Tm (Pmoj: )Tj /T1_0 1 Tf 0.0399 Tc 9.3 0 0 9.3 43.16 500.59 Tm (For )Tj 0.05 Tc 9.5174 0 0 9.3 60.56 500.59 Tm (any )Tj /T1_1 1 Tf 0.0295 Tc 9.6 0 0 9.6 79.31 500.59 Tm (x, )Tj 0 Tc 9 0 0 9 89.14 500.59 Tm (y )Tj /T1_0 1 Tf 8.4 0 0 8.4 96.97 500.59 Tm (E )Tj /T1_2 1 Tf -0.035 Tc 8.7796 0 0 9 105.96 500.59 Tm (Zp, )Tj /T1_0 1 Tf 8.9557 0 0 9.3 122.03 500.59 Tm (we )Tj 0.0178 Tc 9.3 0 0 9.3 135.89 500.59 Tm (have )Tj 0.05 Tc 9.3717 0 0 9.3 12.7 454.69 Tm (Therefore )Tj /T1_2 1 Tf 0 Tc 12 0 0 12 57.44 454.69 Tm (f )Tj /T1_0 1 Tf -0.0111 Tc 9.3 0 0 9.3 66.34 454.69 Tm (is )Tj 0.05 Tc 9.5322 0 0 9.3 76.58 454.69 Tm (an )Tj 0.0371 Tc 9.3 0 0 9.3 89.74 454.69 Tm (isomorphism )Tj 0.0373 Tc 5.971 0 Td (between )Tj /T1_2 1 Tf -0.0112 Tc 9.6 0 0 9.6 182.43 454.69 Tm (Gp\(S\) )Tj /T1_0 1 Tf 0.05 Tc 9.8699 0 0 9.3 212.12 454.69 Tm (and )Tj /T1_2 1 Tf 0.0034 Tc 9.6 0 0 9.6 231.03 454.69 Tm (Gp\(S*\). )Tj /T1_0 1 Tf 0.05 Tc 10.6147 0 0 9.5 12.84 426.61 Tm (3. )Tj 10.8034 0 0 9.5 27.23 426.61 Tm (Normalized )Tj 10.0339 0 0 9.5 87.38 426.61 Tm (Cyclic )Tj 10.8394 0 0 9.5 120.31 426.61 Tm (Graphs )Tj 11.0596 0 0 9.5 158.29 426.61 Tm (of )Tj 11.3435 0 0 9.5 171.31 426.61 Tm (Prime )Tj 11.3364 0 0 9.5 205.09 426.61 Tm (Order )Tj -0.0339 Tc 9.3 0 0 9.3 33.12 409.15 Tm (\\Ve )Tj 0.0446 Tc 1.81 0 Td (consider )Tj 0.0338 Tc 4.123 0 Td (only )Tj /T1_1 1 Tf 0 Tc 9.8 0 0 9.8 109.68 409.15 Tm (t )Tj /T1_2 1 Tf 0.0263 Tc 8.1 0 0 8.1 127.38 409.15 Tm (lSI )Tj /T1_0 1 Tf -0.035 Tc 5.7818 0 0 10.6 142.35 409.15 Tm (2:: )Tj 8.7919 0 0 9.3 152.59 409.15 Tm (2. )Tj 0.0476 Tc 9.3 0 0 9.3 165.19 409.15 Tm (Let )Tj /T1_2 1 Tf 0 Tc 7.9001 0 0 7.9001 182.82 409.15 Tm (g )Tj /T1_0 1 Tf 0.05 Tc 9.5181 0 0 9.3 191.53 409.15 Tm (be )Tj 0 Tc 9.3 0 0 9.3 205.29 409.15 Tm (a )Tj 0.05 Tc 9.4176 0 0 9.3 213.85 409.15 Tm (primitive )Tj 9.513 0 0 9.3 255.95 409.15 Tm (root )Tj 0.0443 Tc 9.3 0 0 9.3 277.36 409.15 Tm (modulo )Tj /T1_2 1 Tf 0.0131 Tc 7.9001 0 0 7.9001 311.25 409.15 Tm (p, )Tj /T1_0 1 Tf -0.0121 Tc 9.3 0 0 9.3 322.07 409.15 Tm (so )Tj /T1_2 1 Tf -0.0103 Tc 8.1 0 0 8.1 334.57 409.15 Tm (Z:\); )Tj /T1_1 1 Tf 0 Tc 12.1 0 0 12.1 350.83 409.15 Tm (= )Tj /T1_3 1 Tf -0.035 Tc 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/T1_3 1 Tf -0.035 Tc 5.4731 0 0 10.2 72.04 481.5099 Tm (:2: )Tj /T1_0 1 Tf -0.0125 Tc 9.3 0 0 9.3 82.15 481.5099 Tm (96, )Tj /T1_2 1 Tf 0.05 Tc 9.5496 0 0 9.5 98.15 481.5099 Tm (R\( )Tj /T1_0 1 Tf 9.6839 0 0 9.3 109.58 481.5099 Tm (4,12\) )Tj /T1_3 1 Tf -0.035 Tc 5.6556 0 0 10.2 135.75 481.5099 Tm (:2: )Tj /T1_0 1 Tf 0.0018 Tc 9.3 0 0 9.3 146.02 481.5099 Tm (106, )Tj /T1_2 1 Tf 0.05 Tc 9.5496 0 0 9.5 166.55 481.5099 Tm (R\( )Tj /T1_0 1 Tf -0.0186 Tc 9.3 0 0 9.3 178.16 481.5099 Tm (4, )Tj 0.0079 Tc 1.073 0 Td (13\) )Tj /T1_3 1 Tf -0.035 Tc 5.6556 0 0 10.2 204.87 481.5099 Tm (:2: )Tj /T1_0 1 Tf -0.0176 Tc 9.3 0 0 9.3 215.5 481.5099 Tm (118, )Tj /T1_2 1 Tf 0.0178 Tc 9.5 0 0 9.5 235.49 481.5099 Tm (R\( )Tj /T1_0 1 Tf -0.035 Tc 9.0039 0 0 9.3 246.74 481.5099 Tm (4, )Tj -0.0308 Tc 9.3 0 0 9.3 256.18 481.5099 Tm (14\) )Tj /C0_0 1 Tf 0 Tc 6.1201 0 0 7.3801 272.35 481.5099 Tm <007E0020>Tj /T1_0 1 Tf -0.024 Tc 9.3 0 0 9.3 283.36 481.5099 Tm (129, )Tj /T1_2 1 Tf 0.05 Tc 9.7142 0 0 9.5 302.81 481.5099 Tm (R\( )Tj /T1_0 1 Tf -0.035 Tc 9.0039 0 0 9.3 314.78 481.5099 Tm (4, )Tj 0.0079 Tc 9.3 0 0 9.3 324.04 481.5099 Tm (15\) )Tj /C0_0 1 Tf 0 Tc 6.1201 0 0 7.3801 341.11 481.5099 Tm <007E0020>Tj /T1_0 1 Tf -0.0047 Tc 9.3 0 0 9.3 351.94 481.5099 Tm (134. )Tj 0.05 Tc 9.536 0 0 9.3 373.97 481.5099 Tm (In )Tj 0.007 Tc 9.3 0 0 9.3 35.14 470.17 Tm (1997, )Tj 0.0223 Tc 2.745 0 Td (Su, )Tj 0.0357 Tc 1.832 0 Td (Luo, )Tj -0.0038 Tc 2.497 0 Td (Li )Tj -0.035 Tc 7.1607 0 0 9.3 113.77 470.17 Tm ([9} )Tj 0.05 Tc 9.4069 0 0 9.3 127.35 470.17 Tm (obtained )Tj /T1_2 1 Tf 9.7142 0 0 9.5 167.45 470.17 Tm (R\( )Tj /T1_0 1 Tf 9.6839 0 0 9.3 179.06 470.17 Tm (4,12\) )Tj /T1_3 1 Tf -0.035 Tc 5.838 0 0 10.2 206.13 470.17 Tm (:2: )Tj /T1_0 1 Tf -0.0176 Tc 9.3 0 0 9.3 217.12 470.17 Tm (128. )Tj 0.05 Tc 9.3321 0 0 9.3 239.5 470.17 Tm (This )Tj 0.0353 Tc 9.3 0 0 9.3 261.64 470.17 Tm (implies )Tj 0.05 Tc 10.0691 0 0 9.3 295 470.17 Tm (that )Tj /T1_2 1 Tf -0.0011 Tc 9.5 0 0 9.5 316.67 470.17 Tm (R\( )Tj /T1_0 1 Tf 0.05 Tc 9.8426 0 0 9.3 327.56 470.17 Tm (4,13\) )Tj /T1_3 1 Tf -0.035 Tc 5.4731 0 0 10.2 355.18 470.17 Tm (:2: )Tj /T1_0 1 Tf 0.0018 Tc 9.3 0 0 9.3 365.98 470.17 Tm (131, )Tj /T1_2 1 Tf 0.0368 Tc 9.5 0 0 9.5 34.97 458.2899 Tm (R\( )Tj /T1_0 1 Tf 0.05 Tc 9.3664 0 0 9.3 46.22 458.2899 Tm (4,14\) )Tj /T1_3 1 Tf -0.035 Tc 5.4731 0 0 10.2 71.86 458.2899 Tm (:2: )Tj /T1_0 1 Tf 0.0082 Tc 9.3 0 0 9.3 81.58 458.2899 Tm (136, )Tj /T1_2 1 Tf 0.0368 Tc 9.5 0 0 9.5 101.93 458.2899 Tm (R\( )Tj /T1_0 1 Tf 0.05 Tc 9.4457 0 0 9.3 113.36 458.2899 Tm (4,15\) )Tj /T1_3 1 Tf -0.035 Tc 5.838 0 0 10.2 138.81 458.2899 Tm (:2: )Tj /T1_0 1 Tf 0.0018 Tc 9.3 0 0 9.3 148.72 458.2899 Tm (145 )Tj 0.05 Tc 9.3426 0 0 9.3 166.51 458.2899 Tm (by )Tj 9.36 0 0 9.3 180.36 458.2899 Tm (using )Tj 9.4259 0 0 9.3 206.44 458.2899 Tm (the )Tj 0.0391 Tc 9.3 0 0 9.3 222.75 458.2899 Tm (observation )Tj 0.0122 Tc 5.514 0 Td (\(see )Tj -0.035 Tc 8.8842 0 0 9.3 293.37 458.2899 Tm ([8]\): )Tj /T1_3 1 Tf 0.05 Tc 12.1279 0 0 9.1 47.37 432.7299 Tm (If )Tj /T1_2 1 Tf 0.0493 Tc 9.5 0 0 9.5 64.49 432.7299 Tm (R\(k,p\) )Tj /C0_0 1 Tf 0 Tc 5.9401 0 0 7.3801 97.21 432.7299 Tm <007E0020>Tj /T1_0 1 Tf 0.05 Tc 14.6263 0 0 9.3 107.25 432.7299 Tm (sand )Tj /T1_2 1 Tf 0.0375 Tc 9.5 0 0 9.5 146.21 432.7299 Tm (R\(k, )Tj 0.05 Tc 7.8109 0 0 7.7 167.46 432.7299 Tm (q\) )Tj /C0_0 1 Tf 0 Tc 5.9401 0 0 7.3801 179.29 432.7299 Tm <007E0020>Tj /T1_1 1 Tf 0.0011 Tc 10 0 0 10 189.24 432.7299 Tm (t, )Tj /T1_0 1 Tf 0.05 Tc 9.6378 0 0 9.3 207.16 432.7299 Tm (then )Tj /T1_2 1 Tf 9.642 0 0 9.5 235.31 432.7299 Tm (R\(k,p )Tj /T1_3 1 Tf 0 Tc 11.9 0 0 11.9 262.79 432.7299 Tm (+ )Tj /T1_2 1 Tf 7.7 0 0 7.7 272.23 432.7299 Tm (q )Tj /T1_0 1 Tf -0.035 Tc 9.1661 0 0 9.3 289.3 432.7299 Tm (1\) )Tj 7.219 0 0 10.4 300.38 432.7299 Tm (2: )Tj 6.2128 0 0 10.4 310.01 432.7299 Tm (.., )Tj /T1_3 1 Tf 0 Tc 11.9 0 0 11.9 317.51 432.7299 Tm (+ )Tj /T1_1 1 Tf 10 0 0 10 326.58 432.7299 Tm (t )Tj /T1_3 1 Tf -0.0254 Tc 8.5 0 0 8.5 342.81 432.7299 Tm (1. )Tj /T1_0 1 Tf 0.0144 Tc 9.3 0 0 9.3 363.67 432.7299 Tm (\(1.1\) )Tj 0.0188 Tc -33.222 -2.826 Td (Using )Tj 0.0268 Tc 2.798 0 Td (cyclic )Tj 0.05 Tc 9.4336 0 0 9.3 107.2 406.45 Tm (graphs )Tj 0.039 Tc 9.3 0 0 9.3 137.61 406.45 Tm (of )Tj 0.05 Tc 9.5677 0 0 9.3 147.79 406.45 Tm (prime )Tj 9.6741 0 0 9.3 175.05 406.45 Tm (order )Tj 9.6041 0 0 9.3 200.68 406.45 Tm (to )Tj 9.5724 0 0 9.3 211.77 406.45 Tm (obtain )Tj -0.0085 Tc 9.3 0 0 9.3 241.12 406.45 Tm (lower )Tj 0.05 Tc 9.4907 0 0 9.3 265.15 406.45 Tm (bounds )Tj -0.0216 Tc 9.3 0 0 9.3 297.98 406.45 Tm (for )Tj 0.042 Tc 1.53 0 Td (classical )Tj 0.05 Tc 9.4007 0 0 9.3 349.88 406.45 Tm (Ramsey )Tj 9.3883 0 0 9.3 35.45 394.75 Tm (numbers )Tj 9.3271 0 0 9.3 74.87 394.75 Tm (has )Tj 9.5046 0 0 9.3 92.71 394.75 Tm (been )Tj 0.0326 Tc 9.3 0 0 9.3 116.54 394.75 Tm (fruitful )Tj 0.05 Tc 9.5456 0 0 9.3 149.68 394.75 Tm (in )Tj 9.8357 0 0 9.3 161.8 394.75 Tm (the )Tj 9.6586 0 0 9.3 179.47 394.75 Tm (past. )Tj -0.0245 Tc 9.3 0 0 9.3 206.79 394.75 Tm (We )Tj 0.0127 Tc 1.86 0 Td (refer )Tj 0.05 Tc 9.6041 0 0 9.3 246.58 394.75 Tm (to )Tj -0.035 Tc 7.8545 0 0 9.3 259.29 394.75 Tm (\(2] )Tj 0.0171 Tc 9.3 0 0 9.3 272.78 394.75 Tm (for )Tj 0.05 Tc 9.3236 0 0 9.3 288.7 394.75 Tm (theoretical )Tj 9.5401 0 0 9.3 337.3 394.75 Tm (motivation )Tj 9.5174 0 0 9.3 35.54 383.05 Tm (and )Tj 9.6093 0 0 9.3 53.55 383.05 Tm (computational )Tj 0.026 Tc 9.3 0 0 9.3 117.08 383.05 Tm (evidence. )Tj 0.05 Tc 9.536 0 0 9.3 159.59 383.05 Tm (In )Tj 9.6187 0 0 9.3 171.7 383.05 Tm (this )Tj 9.4982 0 0 9.3 190.63 383.05 Tm (paper, )Tj -0.035 Tc 9.1156 0 0 9.3 220.13 383.05 Tm (we )Tj 0.0188 Tc 9.3 0 0 9.3 233.72 383.05 Tm (first )Tj 0.05 Tc 9.6893 0 0 9.3 253.12 383.05 Tm (study )Tj 0.0086 Tc 9.3 0 0 9.3 279.59 383.05 Tm (some )Tj 0.05 Tc 9.6574 0 0 9.3 302.41 383.05 Tm (properties )Tj 9.8076 0 0 9.3 348.93 383.05 Tm (of )Tj 0.0152 Tc 9.3 0 0 9.3 359.73 383.05 Tm (cyclic )Tj 0.05 Tc 9.3715 0 0 9.3 35.56 371.53 Tm (graphs )Tj 0.0197 Tc 9.3 0 0 9.3 67.77 371.53 Tm (of )Tj 0.05 Tc 9.6391 0 0 9.3 79.75 371.53 Tm (prime )Tj 9.5168 0 0 9.3 108.99 371.53 Tm (order )Tj 9.5174 0 0 9.3 135.62 371.53 Tm (and )Tj 9.5698 0 0 9.3 155.8 371.53 Tm (introduce )Tj 0 Tc 9.3 0 0 9.3 201.15 371.53 Tm (a )Tj 0.0358 Tc 0.983 0 Td (special )Tj 0.0182 Tc 3.488 0 Td (class )Tj 0.05 Tc 9.3902 0 0 9.3 266.49 371.53 Tm (of )Tj 0.0388 Tc 9.3 0 0 9.3 279.34 371.53 Tm (them, )Tj 0.05 Tc 9.5472 0 0 9.3 307.61 371.53 Tm (normalized )Tj 0.0152 Tc 9.3 0 0 9.3 359.73 371.53 Tm (cyclic )Tj 0.05 Tc 9.3715 0 0 9.3 35.56 359.83 Tm (graphs )Tj 0.039 Tc 9.3 0 0 9.3 67.23 359.83 Tm (of )Tj 0.05 Tc 9.6391 0 0 9.3 78.67 359.83 Tm (prime )Tj 9.3178 0 0 9.3 107.19 359.83 Tm (order, )Tj 0.0327 Tc 9.3 0 0 9.3 136 359.83 Tm (in )Tj 0.0495 Tc 1.268 0 Td (Sections )Tj 0 Tc 4.232 0 Td (2 )Tj 0.05 Tc 9.6349 0 0 9.3 196.1 359.83 Tm (and )Tj -0.035 Tc 9.2907 0 0 9.3 215.71 359.83 Tm (3. )Tj -0.0245 Tc 9.3 0 0 9.3 229.47 359.83 Tm (We )Tj 0.0144 Tc 1.828 0 Td (show )Tj 0.05 Tc 10.3974 0 0 9.3 271.05 359.83 Tm (that )Tj 0.0357 Tc 9.3 0 0 9.3 292.76 359.83 Tm (every )Tj 0.0229 Tc 2.827 0 Td (cyclic )Tj 0.05 Tc 9.6535 0 0 9.3 347.14 359.83 Tm (graph )Tj 0.039 Tc 9.3 0 0 9.3 375.39 359.83 Tm (of )Tj 0.05 Tc 9.4249 0 0 9.3 35.65 347.95 Tm (prime )Tj 9.3595 0 0 9.3 63.81 347.95 Tm (order )Tj -0.0111 Tc 9.3 0 0 9.3 89.92 347.95 Tm (is )Tj 0.0399 Tc 1.181 0 Td (isomorphic )Tj 0.05 Tc 10.0407 0 0 9.3 150.82 347.95 Tm (to )Tj 9.4281 0 0 9.3 163.67 347.95 Tm (some )Tj 0.0452 Tc 9.3 0 0 9.3 190.07 347.95 Tm (normalized )Tj 0.0074 Tc 5.391 0 Td (cyclic )Tj 0.05 Tc 9.6535 0 0 9.3 267.58 347.95 Tm (graph )Tj -0.0191 Tc 9.3 0 0 9.3 296.01 347.95 Tm (of )Tj 0.05 Tc 9.6391 0 0 9.3 307.63 347.95 Tm (prime )Tj 9.4569 0 0 9.3 336.87 347.95 Tm (order. )Tj -0.0245 Tc 9.3 0 0 9.3 369.87 347.95 Tm (We )Tj 0.05 Tc 9.5414 0 0 9.3 35.98 336.0699 Tm (then )Tj 0.0385 Tc 9.3 0 0 9.3 57.97 336.0699 Tm (propose )Tj 0.05 Tc 10.0821 0 0 9.3 93.68 336.0699 Tm (an )Tj 9.394 0 0 9.3 107.9 336.0699 Tm (algorithm )Tj 9.8224 0 0 9.3 152.26 336.0699 Tm (to )Tj 0.0311 Tc 9.3 0 0 9.3 164.24 336.0699 Tm (find )Tj 0.0208 Tc 2.187 0 Td (effective )Tj 0.05 Tc 9.5688 0 0 9.3 222.67 336.0699 Tm (parameter )Tj 9.5394 0 0 9.3 268.61 336.0699 Tm (sets )Tj -0.035 Tc 9.2002 0 0 9.3 288.26 336.0699 Tm (for )Tj 0.05 Tc 9.8082 0 0 9.3 302.3 336.0699 Tm (constructing )Tj 0.0152 Tc 9.3 0 0 9.3 359.91 336.0699 Tm (cyclic )Tj 0.05 Tc 9.3094 0 0 9.3 35.92 324.55 Tm (graphs )Tj 0.0197 Tc 9.3 0 0 9.3 66.87 324.55 Tm (of )Tj 0.05 Tc 9.4963 0 0 9.3 77.59 324.55 Tm (prime )Tj 9.5954 0 0 9.3 105.39 324.55 Tm (order )Tj -0.006 Tc 9.3 0 0 9.3 131.14 324.55 Tm (in )Tj 0.0484 Tc 1.171 0 Td (Section )Tj -0.0186 Tc 3.711 0 Td (4. )Tj 0.05 Tc 9.8989 0 0 9.3 188.74 324.55 Tm (The )Tj 0.0111 Tc 9.3 0 0 9.3 209.15 324.55 Tm (new )Tj 0.05 Tc 9.394 0 0 9.3 228.68 324.55 Tm (algorithm )Tj 0.0303 Tc 9.3 0 0 9.3 272.33 324.55 Tm (reduces )Tj 0.05 Tc 9.7933 0 0 9.3 306.44 324.55 Tm (certain )Tj 9.7901 0 0 9.3 339.74 324.55 Tm (amount )Tj 0.039 Tc 9.3 0 0 9.3 375.57 324.55 Tm (of )Tj 0.05 Tc 9.5361 0 0 9.3 35.91 313.03 Tm (computation )Tj 9.3902 0 0 9.3 91.53 313.03 Tm (of )Tj 0.019 Tc 9.3 0 0 9.3 102.69 313.03 Tm (cyclic )Tj 0.0467 Tc 2.885 0 Td (graphs )Tj 0.05 Tc 9.3902 0 0 9.3 159.93 313.03 Tm (of )Tj 9.6391 0 0 9.3 171.19 313.03 Tm (prime )Tj 0.0394 Tc 9.3 0 0 9.3 198.99 313.03 Tm (order, )Tj 0.0256 Tc 2.957 0 Td (since )Tj 0.0274 Tc 2.52 0 Td (only )Tj 0.0474 Tc 2.202 0 Td (some )Tj -0.0191 Tc (of )Tj 0.05 Tc 10.0716 0 0 9.3 304.9 313.03 Tm (them )Tj 0 Tc 9.3 0 0 9.3 329.83 313.03 Tm (-)Tj 0.05 Tc 9.3286 0 0 9.3 336.77 313.03 Tm (normalized )Tj 0.0113 Tc 9.3 0 0 9.3 36.09 301.69 Tm (cyclic )Tj 0.0467 Tc 2.904 0 Td (graphs )Tj 0.0479 Tc 3.414 0 Td (require )Tj 0.05 Tc 9.5083 0 0 9.3 128.61 301.69 Tm (computation. )Tj 9.4167 0 0 9.3 191.48 301.69 Tm (For )Tj 9.5625 0 0 9.3 209.68 301.69 Tm (the )Tj 0.0155 Tc 9.3 0 0 9.3 227.14 301.69 Tm (two-color )Tj 0.0498 Tc 4.508 0 Td (Ramsey )Tj 0.05 Tc 9.4955 0 0 9.3 305.65 301.69 Tm (problems, )Tj 0.0428 Tc 9.3 0 0 9.3 352.54 301.69 Tm (it )Tj -0.0305 Tc 1.123 0 Td (is )Tj 0.05 Tc 9.7155 0 0 9.3 373.4 301.69 Tm (an )Tj 0.0438 Tc 9.3 0 0 9.3 36.1 290.17 Tm (improvement )Tj 0.05 Tc 9.5989 0 0 9.3 93.15 290.17 Tm (of )Tj 9.6991 0 0 9.3 104.38 290.17 Tm (the )Tj 9.4362 0 0 9.3 120.68 290.17 Tm (algorithm )Tj 9.3236 0 0 9.3 164.62 290.17 Tm (in )Tj -0.0202 Tc 9.3 0 0 9.3 176.36 290.17 Tm ([10]. )Tj 0.0324 Tc 2.386 0 Td (Several )Tj 0.0418 Tc 3.53 0 Td (examples )Tj 0.05 Tc 10.0407 0 0 9.3 272.68 290.17 Tm (to )Tj 9.3511 0 0 9.3 284.68 290.17 Tm (illustrate )Tj 9.9723 0 0 9.3 325.06 290.17 Tm (the )Tj 9.5204 0 0 9.3 342.26 290.17 Tm (algorithm )Tj 0.0347 Tc 9.3 0 0 9.3 36.27 278.64 Tm (are )Tj 0.0338 Tc 1.714 0 Td (provided. )Tj 0.0382 Tc 4.778 0 Td (Using )Tj 0.05 Tc 9.4259 0 0 9.3 124.36 278.64 Tm (the )Tj 9.4863 0 0 9.3 141.02 278.64 Tm (algorithm, )Tj 0.0007 Tc 9.3 0 0 9.3 188.81 278.64 Tm (we )Tj 0.05 Tc 9.3965 0 0 9.3 203.67 278.64 Tm (construct )Tj 9.4259 0 0 9.3 246.4 278.64 Tm (ten )Tj 0.019 Tc 9.3 0 0 9.3 262.71 278.64 Tm (cyclic )Tj 0.05 Tc 9.4336 0 0 9.3 289.9 278.64 Tm (graphs )Tj 9.3902 0 0 9.3 321.21 278.64 Tm (of )Tj 9.7819 0 0 9.3 332.66 278.64 Tm (prime )Tj 0.0488 Tc 9.3 0 0 9.3 361.35 278.64 Tm (order )Tj 0.05 Tc 9.6041 0 0 9.3 36.16 267.13 Tm (to )Tj 9.5064 0 0 9.3 47.97 267.13 Tm (obtain )Tj 0.0208 Tc 9.3 0 0 9.3 78.11 267.13 Tm (new )Tj 0.0109 Tc 2.18 0 Td (lower )Tj 0.05 Tc 9.3757 0 0 9.3 124.39 267.13 Tm (bounds )Tj 9.3902 0 0 9.3 157.77 267.13 Tm (of )Tj 10.1089 0 0 9.3 169.36 267.13 Tm (ten )Tj 0.0323 Tc 9.3 0 0 9.3 186.75 267.13 Tm (classical )Tj 0.0459 Tc 4.07 0 Td (Ramsey )Tj 0.0399 Tc 3.894 0 Td (numbers. )Tj 0.05 Tc 9.5709 0 0 9.3 303.81 267.13 Tm (We )Tj 0.0371 Tc 9.3 0 0 9.3 321.58 267.13 Tm (list )Tj 0.05 Tc 10.2456 0 0 9.3 338.37 267.13 Tm (the )Tj 0.046 Tc 9.3 0 0 9.3 356.03 267.13 Tm (results )Tj 0.0327 Tc -34.382 -1.239 Td (in )Tj 0.05 Tc 9.4407 0 0 9.3 47.26 255.61 Tm (Theorem )Tj 0.0206 Tc 9.3 0 0 9.3 87.88 255.61 Tm (1.1, )Tj 0.0438 Tc 1.949 0 Td (which )Tj 0.0064 Tc 2.981 0 Td (will )Tj 0.05 Tc 9.335 0 0 9.3 151.93 255.61 Tm (be )Tj 9.367 0 0 9.3 165.25 255.61 Tm (proved )Tj 9.3236 0 0 9.3 197.56 255.61 Tm (in )Tj 0.0387 Tc 9.3 0 0 9.3 208.81 255.61 Tm (Section )Tj -0.035 Tc 8.6466 0 0 9.3 242.52 255.61 Tm (5: )Tj 0.05 Tc 10.8753 0 0 9.3 36.45 234.19 Tm (Theorem )Tj 9.9202 0 0 9.3 82.28 234.19 Tm (1.1. )Tj /T1_2 1 Tf 8.8835 0 0 8.7 105 234.19 Tm (R\(3, )Tj /T1_0 1 Tf -0.019 Tc 9.3 0 0 9.3 125.89 234.19 Tm (31\) )Tj /T1_3 1 Tf -0.035 Tc 5.6556 0 0 10.2 141.69 234.19 Tm (:2: )Tj /T1_0 1 Tf 0.0115 Tc 9.3 0 0 9.3 151.78 234.19 Tm (198)Tj 0 Tc 1.581 0.194 Td (t)Tj 0.529 -0.194 Td (, )Tj /T1_2 1 Tf 0.05 Tc 9.8789 0 0 8.7 176.27 234.19 Tm (R\( )Tj /T1_0 1 Tf 9.5251 0 0 9.3 188.06 234.19 Tm (4,17\) )Tj -0.035 Tc 7.9658 0 0 10.4 213.97 234.19 Tm (2: )Tj 0.05 Tc 9.3524 0 0 9.3 223.96 234.19 Tm (182t, )Tj /T1_2 1 Tf 0.0367 Tc 8.7 0 0 8.7 247.92 234.19 Tm (R\(5, )Tj /T1_0 1 Tf 0.0273 Tc 9.3 0 0 9.3 268.24 234.19 Tm (16\) )Tj /T1_3 1 Tf -0.035 Tc 5.838 0 0 10.2 284.61 234.19 Tm (:2: )Tj /T1_0 1 Tf 0.0036 Tc 9.3 0 0 9.3 294.25 234.19 Tm (278, )Tj /T1_2 1 Tf -0.0065 Tc 9.5 0 0 9.5 314.15 234.19 Tm (R\(5, )Tj /T1_0 1 Tf 0.0204 Tc 9.3 0 0 9.3 334.93 234.19 Tm (20\) )Tj -0.035 Tc 7.7168 0 0 10.4 352.04 234.19 Tm (2: )Tj 0.0039 Tc 9.3 0 0 9.3 361.69 234.19 Tm (380)Tj 0 Tc 1.597 0.155 Td (t)Tj 0.529 -0.155 Td (, )Tj /T1_2 1 Tf -0.0128 Tc 9.5 0 0 9.5 36.59 220.8699 Tm (R\(5, )Tj /T1_0 1 Tf -0.0183 Tc 9.3 0 0 9.3 57.01 220.8699 Tm (25\) )Tj /C0_0 1 Tf 0 Tc 6.1201 0 0 10.08 73.45 220.8699 Tm <007E0020>Tj /T1_0 1 Tf 0.0089 Tc 9.3 0 0 9.3 84.02 220.8699 Tm (458, )Tj /T1_2 1 Tf 0.0062 Tc 9.5 0 0 9.5 105.17 220.8699 Tm (R\(7, )Tj /T1_0 1 Tf -0.0308 Tc 9.3 0 0 9.3 126.22 220.8699 Tm (15\) )Tj /T1_3 1 Tf -0.035 Tc 5.838 0 0 10.2 142.41 220.8699 Tm (:2: )Tj /T1_0 1 Tf 0.0089 Tc 9.3 0 0 9.3 153.14 220.8699 Tm (444, )Tj /T1_2 1 Tf 0.0338 Tc 9.5 0 0 9.5 174.29 220.8699 Tm (R\(7,16\) )Tj /T1_3 1 Tf -0.035 Tc 5.838 0 0 10.2 212.61 220.8699 Tm (:2: )Tj /T1_0 1 Tf -0.004 Tc 9.3 0 0 9.3 222.98 220.8699 Tm (462, )Tj /T1_2 1 Tf -0.0128 Tc 9.5 0 0 9.5 243.77 220.8699 Tm (R\(8, )Tj /T1_0 1 Tf 0.0176 Tc 9.3 0 0 9.3 264.28 220.8699 Tm (13\) )Tj -0.035 Tc 7.4679 0 0 10.4 281.66 220.8699 Tm (2: )Tj -0.0105 Tc 9.3 0 0 9.3 291.56 220.8699 Tm (422, )Tj /T1_2 1 Tf 0.0307 Tc 9.5 0 0 9.5 312.71 220.8699 Tm (R\(8,15\) )Tj /T1_0 1 Tf -0.035 Tc 7.9658 0 0 10.4 351.31 220.8699 Tm (2: )Tj 0.0171 Tc 9.3 0 0 9.3 361.51 220.8699 Tm (618)Tj 0 Tc 1.616 0.155 Td (t)Tj 0.529 -0.155 Td (, )Tj /T1_2 1 Tf -0.0207 Tc 9.5 0 0 9.5 36.59 209.35 Tm (R\(10, )Tj /T1_0 1 Tf -0.0211 Tc 9.3 0 0 9.3 61.78 209.35 Tm (16\) )Tj /C0_0 1 Tf 0 Tc 5.9401 0 0 7.5601 77.58 209.35 Tm <007E0020>Tj /T1_0 1 Tf 0.0215 Tc 9.3 0 0 9.3 87.34 209.35 Tm (1052. )Tj 0.05 Tc 9.459 0 0 9.3 36.64 182.17 Tm (The )Tj -0.0004 Tc 9.3 0 0 9.3 56.96 182.17 Tm (four )Tj 0.05 Tc 9.4907 0 0 9.3 77.59 182.17 Tm (bounds )Tj 0.0481 Tc 9.3 0 0 9.3 112.3 182.17 Tm (marked )Tj 0.05 Tc 9.6485 0 0 9.3 147.23 182.17 Tm (with )Tj /T1_3 1 Tf 0.0206 Tc 11.9 0 0 11.9 171.38 182.17 Tm ("t" )Tj /T1_0 1 Tf 0.05 Tc 9.4959 0 0 9.3 189.62 182.17 Tm (are )Tj 9.8115 0 0 9.3 206.65 182.17 Tm (better )Tj 9.7342 0 0 9.3 236.14 182.17 Tm (than )Tj 9.6991 0 0 9.3 259 182.17 Tm (the )Tj 0.0354 Tc 9.3 0 0 9.3 276.85 182.17 Tm (previously )Tj 0.05 Tc 9.5512 0 0 9.3 323.62 182.17 Tm (known )Tj 0.0428 Tc 9.3 0 0 9.3 356.21 182.17 Tm (results )Tj -0.0071 Tc -34.288 -1.258 Td (\(see )Tj -0.035 Tc 8.7443 0 0 9.3 56.67 170.47 Tm ([8]\) )Tj 0.05 Tc 9.6349 0 0 9.3 73.16 170.47 Tm (and )Tj 9.9723 0 0 9.3 92.32 170.47 Tm (the )Tj 0.0478 Tc 9.3 0 0 9.3 109.79 170.47 Tm (remaining )Tj 0.05 Tc 9.6633 0 0 9.3 155.17 170.47 Tm (bounds )Tj 9.6797 0 0 9.3 189.98 170.47 Tm (appear )Tj -0.012 Tc 9.3 0 0 9.3 222.38 170.47 Tm (for )Tj 0.05 Tc 9.4259 0 0 9.3 237.58 170.47 Tm (the )Tj 0.0188 Tc 9.3 0 0 9.3 254.06 170.47 Tm (first )Tj 0.0268 Tc 2.234 0 Td (time. )Tj 0.05 Tc 9.3386 0 0 9.3 300.77 170.47 Tm (Using )Tj 9.7647 0 0 9.3 329.14 170.47 Tm (Theorem )Tj -0.028 Tc 9.3 0 0 9.3 371.74 170.47 Tm (1.1 )Tj 0.05 Tc 9.5174 0 0 9.3 36.8 158.77 Tm (and )Tj 0.008 Tc 9.3 0 0 9.3 55.51 158.77 Tm (\(1.1\), )Tj -0.035 Tc 9.1156 0 0 9.3 79.91 158.77 Tm (we )Tj 0.05 Tc 9.8365 0 0 9.3 93.69 158.77 Tm (obtain )Tj -0.0083 Tc 9.3 0 0 9.3 124.19 158.77 Tm (new )Tj 0.0254 Tc 2.005 0 Td (lower )Tj 0.05 Tc 9.7208 0 0 9.3 168.49 158.77 Tm (bounds )Tj -0.012 Tc 9.3 0 0 9.3 202.4 158.77 Tm (for )Tj 0.05 Tc 9.4797 0 0 9.3 216.8 158.77 Tm (another )Tj 0.0125 Tc 9.3 0 0 9.3 251.54 158.77 Tm (four )Tj 0.0202 Tc 2.111 0 Td (classical )Tj 0.05 Tc 9.6085 0 0 9.3 307.94 158.77 Tm (Ramsey )Tj 0.0443 Tc 9.3 0 0 9.3 345.05 158.77 Tm (numbers: )Tj 0.05 Tc 10.4388 0 0 9.3 37.15 138.7899 Tm (Corollary )Tj 10.1483 0 0 9.3 85.51 138.7899 Tm (1.2. )Tj /T1_2 1 Tf 0.0125 Tc 9.5 0 0 9.5 108.41 138.7899 Tm (R\(3, )Tj /T1_0 1 Tf -0.019 Tc 9.3 0 0 9.3 129.13 138.7899 Tm (32\) )Tj /C0_0 1 Tf 0 Tc 5.9401 0 0 7.5601 145.09 138.7899 Tm <007E0020>Tj /T1_0 1 Tf 0.0101 Tc 9.3 0 0 9.3 155.11 138.7899 Tm (200, )Tj /T1_2 1 Tf 0.05 Tc 9.7142 0 0 9.5 175.73 138.7899 Tm (R\( )Tj /T1_0 1 Tf 9.4457 0 0 9.3 187.52 138.7899 Tm (4,18\) )Tj /T1_3 1 Tf -0.035 Tc 5.6556 0 0 10.2 213.15 138.7899 Tm (:2: )Tj /T1_0 1 Tf 0.0018 Tc 9.3 0 0 9.3 223.06 138.7899 Tm (185, )Tj /T1_2 1 Tf -0.0191 Tc 9.5 0 0 9.5 243.05 138.7899 Tm (R\(5, )Tj /T1_0 1 Tf 0.001 Tc 9.3 0 0 9.3 263.29 138.7899 Tm (21\) )Tj -0.035 Tc 7.7168 0 0 10.4 279.86 138.7899 Tm (2: )Tj -0.0097 Tc 9.3 0 0 9.3 289.33 138.7899 Tm (384, )Tj /T1_2 1 Tf -0.0002 Tc 9.5 0 0 9.5 309.65 138.7899 Tm (R\(8, )Tj /T1_0 1 Tf 0.0176 Tc 9.3 0 0 9.3 330.52 138.7899 Tm (16\) )Tj /T1_3 1 Tf -0.035 Tc 5.838 0 0 10.2 347.61 138.7899 Tm (:2: )Tj /T1_0 1 Tf 0.0055 Tc 9.3 0 0 9.3 357.37 138.7899 Tm (625. )Tj 0.0237 Tc -34.406 -3.832 Td (2. )Tj 0.05 Tc 10.6558 0 0 9.3 50.33 103.1499 Tm (Isomorphism )Tj 11.477 0 0 9.3 115.99 103.1499 Tm (of )Tj 10.0974 0 0 9.3 129.14 103.1499 Tm (Cyclic )Tj 11.3007 0 0 9.3 162.61 103.1499 Tm (Graphs )Tj 10.8509 0 0 9.3 202.4 103.1499 Tm (of )Tj 11.1334 0 0 9.3 215.05 103.1499 Tm (Prime )Tj 11.1211 0 0 9.3 248.11 103.1499 Tm (Order )Tj 0.0271 Tc 9.3 0 0 9.3 56.25 84.7899 Tm (Given )Tj 0 Tc 2.981 0 Td (a )Tj 0.05 Tc 9.4249 0 0 9.3 92.35 84.7899 Tm (prime )Tj /T1_1 1 Tf 0 Tc 8.7 0 0 8.7 120.17 84.7899 Tm (p )Tj /T1_0 1 Tf 11.2 0 0 11.2 129 84.7899 Tm (= )Tj /T1_1 1 Tf -0.035 Tc 9.0261 0 0 9.4 139.46 84.7899 Tm (27n )Tj /T1_3 1 Tf 0 Tc 12.6 0 0 12.6 155.31 84.7899 Tm (+ )Tj /T1_0 1 Tf -0.0205 Tc 9.3 0 0 9.3 165.64 84.7899 Tm (1, )Tj 0.05 Tc 9.5455 0 0 9.3 176.85 84.7899 Tm (denote )Tj /T1_2 1 Tf -0.035 Tc 8.5893 0 0 8.7 209.1 84.7899 Tm (Zp )Tj /T1_0 1 Tf 0 Tc 11.2 0 0 11.2 223.32 84.7899 Tm (= )Tj 0.05 Tc 11.2115 0 0 9.3 234.26 84.7899 Tm ({-m, )Tj -0.0053 Tc 9.3 0 0 9.3 259.19 84.7899 Tm (... )Tj 0 Tc 0.876 0 Td (, )Tj 0.05 Tc 10.9549 0 0 9.3 271.67 84.7899 Tm (-1,0,1, )Tj 0.0237 Tc 9.3 0 0 9.3 306.53 84.7899 Tm (... )Tj 0 Tc 0.934 0 Td (, )Tj 0.0259 Tc 0.419 0 Td (m} )Tj /T1_3 1 Tf -0.035 Tc 5.9049 0 0 11.6 335.61 84.7899 Tm (== )Tj /T1_0 1 Tf 0.05 Tc 10.9538 0 0 9.3 347.32 84.7899 Tm ([-m, )Tj /T1_2 1 Tf -0.035 Tc 7.7267 0 0 10.4 369.98 84.7899 Tm (Tn]. )Tj /T1_0 1 Tf 9.2388 0 0 9.3 37.41 73.2599 Tm (We )Tj 0.0317 Tc 9.3 0 0 9.3 53.81 73.2599 Tm (write.., )Tj 0 Tc 11.2 0 0 11.2 85.26 73.2599 Tm (= )Tj /T1_1 1 Tf 10 0 0 10 95.28 73.2599 Tm (t )Tj /T1_0 1 Tf 0.0327 Tc 9.3 0 0 9.3 102.52 73.2599 Tm (in )Tj /T1_2 1 Tf 0.0127 Tc 8.7 0 0 8.7 113.88 73.2599 Tm (Zp )Tj /T1_0 1 Tf -0.035 Tc 9.4533 0 0 9.6 128.26 73.2599 Tm (iff )Tj 0 Tc 9.3 0 0 9.3 139.37 73.2599 Tm (s )Tj /T1_3 1 Tf -0.035 Tc 6.0689 0 0 11.6 146.78 73.2599 Tm (== )Tj /T1_1 1 Tf 0 Tc 9.8 0 0 9.8 157.02 73.2599 Tm (t )Tj /T1_0 1 Tf 0.05 Tc 9.8049 0 0 9.3 164.14 73.2599 Tm (mod )Tj /T1_2 1 Tf 8.1823 0 0 8.1 185.79 73.2599 Tm (p. )Tj /T1_0 1 Tf 0.0302 Tc 9.3 0 0 9.3 198.68 73.2599 Tm (For )Tj 0.0389 Tc 1.853 0 Td (any )Tj 0.05 Tc 9.4897 0 0 9.3 234.17 73.2599 Tm (nonempty )Tj 0.0484 Tc 9.3 0 0 9.3 278.87 73.2599 Tm (set )Tj /T1_2 1 Tf 0 Tc 8.7 0 0 8.7 293.58 73.2599 Tm (S )Tj /T1_3 1 Tf 7.5001 0 0 7.5001 303.01 73.2599 Tm (C )Tj /T1_2 1 Tf 0.05 Tc 9.394 0 0 8.7 314.04 73.2599 Tm (Z;; )Tj /T1_0 1 Tf -0.0303 Tc 9.3 0 0 9.3 341.42 73.2599 Tm ([1, )Tj 0.0093 Tc 1.299 0 Td (m], )Tj 0.05 Tc 9.5625 0 0 9.3 370.6 73.2599 Tm (the )Tj 9.4341 0 0 9.3 37.36 61.5699 Tm (graph )Tj /T1_2 1 Tf 0.035 Tc 8.7 0 0 8.7 63.65 61.5699 Tm (Gp\(S\) )Tj /T1_0 1 Tf 0.05 Tc 9.6485 0 0 9.3 91.79 61.5699 Tm (with )Tj 0.0477 Tc 9.3 0 0 9.3 113.38 61.5699 Tm (vertex )Tj 0.05 Tc 9.5798 0 0 9.3 141.7 61.5699 Tm (set )Tj /T1_2 1 Tf 0 Tc 8.7 0 0 8.7 156.64 61.5699 Tm (V )Tj /T1_0 1 Tf 11.8 0 0 11.8 167.52 61.5699 Tm (= )Tj /T1_2 1 Tf -0.0287 Tc 8.7 0 0 8.7 178.14 61.5699 Tm (Zp )Tj /T1_0 1 Tf 0.05 Tc 9.7524 0 0 9.3 191.78 61.5699 Tm (and )Tj 0.0166 Tc 9.3 0 0 9.3 209.96 61.5699 Tm (edge )Tj 0.05 Tc 9.4277 0 0 9.3 231.17 61.5699 Tm (set )Tj /T1_2 1 Tf 0 Tc 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333.15 82.09 Tm (Zhang )Tj -0.035 Tc 8.1464 0 0 9.3 15.46 70.38 Tm ([6] )Tj 0.0291 Tc 9.3 0 0 9.3 29.03 70.38 Tm (showed )Tj 0.05 Tc 10.1785 0 0 9.3 63.34 70.38 Tm (that )Tj /T1_1 1 Tf 0.0154 Tc 9.5 0 0 9.5 84.47 70.38 Tm (R\(3,8\) )Tj /T1_0 1 Tf 0 Tc 11.4 0 0 11.4 116.58 70.38 Tm (= )Tj -0.0237 Tc 9.4 0 0 9.4 127.92 70.38 Tm (28 )Tj 0.05 Tc 9.5157 0 0 9.3 141.49 70.38 Tm (by )Tj 0.0393 Tc 9.3 0 0 9.3 156.24 70.38 Tm (using )Tj 0 Tc 2.797 0 Td (a )Tj 0.05 Tc 9.6698 0 0 9.3 191.02 70.38 Tm (substantial )Tj 9.5676 0 0 9.3 241.64 70.38 Tm (amount )Tj 9.8076 0 0 9.3 277.47 70.38 Tm (of )Tj 0.0442 Tc 9.3 0 0 9.3 289.35 70.38 Tm (computation. )Tj 0.05 Tc 10.5725 0 0 9.3 349.85 70.38 Tm (In )Tj 0.0107 Tc 9.4 0 0 9.4 15.33 58.51 Tm (1995, )Tj 0.0421 Tc 9.3 0 0 9.3 41.36 58.51 Tm (McKay )Tj 0.0485 Tc 3.672 0 Td (and )Tj 0.0254 Tc 2.038 0 Td (Radziszowski )Tj -0.035 Tc 8.3161 0 0 9.4 153.7 58.51 Tm ([5] )Tj 0.0291 Tc 9.3 0 0 9.3 167.63 58.51 Tm (showed )Tj 0.05 Tc 10.2879 0 0 9.3 202.29 58.51 Tm (that )Tj /T1_1 1 Tf 0.0008 Tc 10 0 0 10 223.96 58.51 Tm (R\( )Tj /T1_0 1 Tf 0.05 Tc 9.6408 0 0 9.4 235.4 58.51 Tm (4,5\) )Tj 0 Tc 13 0 0 13 256.97 58.51 Tm (= )Tj -0.0237 Tc 9.4 0 0 9.4 268.32 58.51 Tm (25 )Tj 0.05 Tc 9.4612 0 0 9.3 282.23 58.51 Tm (with )Tj 9.5625 0 0 9.3 304.54 58.51 Tm (the )Tj 0.0215 Tc 9.3 0 0 9.3 321.29 58.51 Tm (help )Tj 0.039 Tc 2.256 0 Td (of )Tj 0 Tc 1.297 0 Td (a )Tj 0.0386 Tc -36.463 -1.258 Td (long )Tj 0.05 Tc 9.3884 0 0 9.3 36.27 46.81 Tm (computer )Tj 0.0212 Tc 9.3 0 0 9.3 77.99 46.81 Tm (search. )Tj 0 Tc 3.476 0 Td (A )Tj 0.05 Tc 9.6009 0 0 9.3 120.23 46.81 Tm (number )Tj 0.039 Tc 9.3 0 0 9.3 155.61 46.81 Tm (of )Tj 0.006 Tc 1.162 0 Td (lower )Tj 0.05 Tc 9.6633 0 0 9.3 191.35 46.81 Tm (bounds )Tj -0.012 Tc 9.3 0 0 9.3 225.26 46.81 Tm (for )Tj 0.05 Tc 9.3488 0 0 9.3 239.72 46.81 Tm (Ramsey )Tj 0.0495 Tc 9.3 0 0 9.3 275.93 46.81 Tm (numbers )Tj 0.0154 Tc 4.133 0 Td (are )Tj 0.0236 Tc 1.633 0 Td (known; )Tj 0.0042 Tc -33.805 -1.277 Td (see )Tj 0.05 Tc 9.6991 0 0 9.3 30.94 34.93 Tm (the )Tj 0.0333 Tc 9.3 0 0 9.3 47.39 34.93 Tm (survey )Tj 0.05 Tc 9.4109 0 0 9.3 77.41 34.93 Tm [(paper )-60(paper )]TJ 9.3426 0 0 9.3 130.33 34.93 Tm (by )Tj 0.0377 Tc 9.3 0 0 9.3 143.96 34.93 Tm (Radziszowski )Tj -0.035 Tc 8.89 0 0 9.3 203.91 34.93 Tm ([8]. )Tj 0.0191 Tc 8.9 0 0 8.9 68.74 11.71 Tm (Australasian )Tj 0.05 Tc 8.9058 0 0 8.9 119.47 11.71 Tm (Journal )Tj 9.1816 0 0 8.9 152.55 11.71 Tm (of )Tj 0.0442 Tc 8.9 0 0 8.9 163.89 11.71 Tm (Combinatorics )Tj 0.0463 Tc 7.043 0 Td (24\(2001\), )Tj 0.05 Tc 9.1744 0 0 8.9 270.37 11.71 Tm (pp.81-90 )Tj ET endstream endobj 113 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 25213/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream *Z *X]F@TF@TF@TF@TF@TG *X# +(`KH2229RGQb" *X#P (A r9R:@TG *XGQ,Q ":K0r$uRPE!b#@TG *X#,Q# ( (KDr +(`KdA 9RR29RGQb.9RGQ@TG *X#,QP (A dKdKu "# *X *X *1P@b@TF@TYB@TF@TF@TF@TBc,Du,QP@2222$uRR *X#,Q# (P@22$uRR]Dr$u!b.222$u!b@TF@TG *X# *X *X]A ( ( 22$uc *X *1,Q# (dJՔ H2 *X# *X *X 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