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(t}. )Tj
0.05 Tc 8.3591 0 0 7.9001 127.01 397.27 Tm
(The )Tj
8.7665 0 0 7.9001 147.94 397.27 Tm
(vertices )Tj
8.9729 0 0 7.9001 185.13 397.27 Tm
(of )Tj
/T1_2 1 Tf
-0.0267 Tc 7.6 0 0 7.6 199.62 397.27 Tm
(H. )Tj
/T1_0 1 Tf
0.05 Tc 9.083 0 0 7.9001 214.47 397.27 Tm
(are )Tj
8.2137 0 0 7.9001 233.75 397.27 Tm
(in )Tj
8.6833 0 0 7.9001 247.85 397.27 Tm
(rows )Tj
/T1_2 1 Tf
8.9622 0 0 7.6 273.35 397.27 Tm
(2i )Tj
0 Tc 7.6 0 0 7.6 288.47 397.27 Tm
(-)Tj
/T1_0 1 Tf
0.05 Tc 8.6949 0 0 7.9001 309.33 397.27 Tm
(and )Tj
0 Tc 5.8001 0 0 5.8001 37.24 392.23 Tm
(1 )Tj
28.924 0 Td
(1 )Tj
0.05 Tc 7.9596 0 0 7.9001 16.51 383.05 Tm
(2i. )Tj
8.2323 0 0 7.9001 37.9 383.05 Tm
(Observe )Tj
9.9596 0 0 7.9001 73.6 383.05 Tm
(that )Tj
8.8795 0 0 7.9001 96.1 383.05 Tm
(the )Tj
8.9231 0 0 7.9001 113.74 383.05 Tm
(vertices )Tj
8.2137 0 0 7.9001 150.77 383.05 Tm
(in )Tj
8.2249 0 0 7.9001 163.54 383.05 Tm
(any )Tj
8.0324 0 0 7.9001 182.08 383.05 Tm
(column )Tj
8.7776 0 0 7.9001 213.92 383.05 Tm
(form )Tj
8.6156 0 0 7.9001 238.59 383.05 Tm
(an )Tj
9.1675 0 0 7.9001 253.43 383.05 Tm
(r-clique )Tj
8.6949 0 0 7.9001 291.33 383.05 Tm
(and )Tj
9.1527 0 0 7.9001 310.84 383.05 Tm
(the )Tj
8.6622 0 0 7.9001 16.72 368.83 Tm
(vertices )Tj
8.4356 0 0 7.9001 54.83 368.83 Tm
(in )Tj
8.8124 0 0 7.9001 69.57 368.83 Tm
(any )Tj
8.8113 0 0 7.9001 91.25 368.83 Tm
(row )Tj
8.9481 0 0 7.9001 113.3 368.83 Tm
(form )Tj
0 Tc 7.9001 0 0 7.9001 139.96 368.83 Tm
(a )Tj
0.05 Tc 8.7624 0 0 7.9001 152.08 368.83 Tm
(triangle. )Tj
8.8345 0 0 7.9001 200.66 369.01 Tm
(Further, )Tj
0 Tc 7.9001 0 0 7.9001 240.76 369.01 Tm
(a )Tj
0.05 Tc 9.1298 0 0 7.9001 252.88 369.01 Tm
(vertex )Tj
0 Tc 7.9001 0 0 7.9001 286.17 369.01 Tm
(x )Tj
0.05 Tc 9.3902 0 0 7.9001 298.89 369.01 Tm
(of )Tj
0.0045 Tc 7.8001 0 0 7.8001 315.15 369.01 Tm
(Hi )Tj
0.05 Tc 8.4644 0 0 7.5001 141.61 355.33 Tm
(2i )Tj
0 Tc 7.5001 0 0 7.5001 154.71 355.33 Tm
[(-)-916(1 )]TJ
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(or )Tj
8.0095 0 0 7.9001 186.25 355.33 Tm
(2i\) )Tj
8.4876 0 0 7.9001 201.89 355.33 Tm
(is )Tj
8.5894 0 0 7.9001 214.04 355.33 Tm
(joined )Tj
9.3858 0 0 7.9001 243.16 355.33 Tm
(to )Tj
8.6278 0 0 7.9001 256.59 355.33 Tm
(every )Tj
9.1955 0 0 7.9001 283.84 355.33 Tm
(vertex )Tj
8.7642 0 0 7.9001 315.28 355.33 Tm
(of )Tj
8.2054 0 0 7.9001 16.57 354.61 Tm
(belonging )Tj
9.1676 0 0 7.9001 58.12 354.61 Tm
(to )Tj
8.4787 0 0 7.9001 71.74 354.61 Tm
(column )Tj
8.3863 0 0 7.9001 104.85 354.61 Tm
(C. )Tj
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(J )Tj
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(except: )Tj
8.9062 0 0 7.9001 68.92 340.75 Tm
(two )Tj
8.8709 0 0 7.9001 90.16 340.75 Tm
(vertices )Tj
8.9729 0 0 7.9001 127.17 340.75 Tm
(of )Tj
-0.0186 Tc 7.8001 0 0 7.8001 141.63 340.75 Tm
(Hi )Tj
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(one )Tj
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(in )Tj
8.0882 0 0 7.9001 187.84 340.75 Tm
(column )Tj
8.3863 0 0 7.9001 16.65 326.89 Tm
(C. )Tj
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(1 )Tj
/T1_0 1 Tf
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(\(the )Tj
9.2 0 0 7.9001 59.45 326.89 Tm
(subscripts )Tj
9.3582 0 0 7.9001 106.46 326.89 Tm
(are )Tj
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(written )Tj
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(modulo )Tj
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7.5493 0 0 7 192.33 326.89 Tm
(3\); )Tj
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8.2249 0 0 7.9001 208.54 326.89 Tm
(any )Tj
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(J+ )Tj
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(not )Tj
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(Hi )Tj
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(lying )Tj
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(in )Tj
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(any )Tj
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(row )Tj
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(above )Tj
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(x; )Tj
0.05 Tc 8.3424 0 0 7.9001 179.02 312.85 Tm
(any )Tj
8.8014 0 0 7.9001 197.8 312.85 Tm
(vertex )Tj
8.8124 0 0 7.9001 242.55 341.29 Tm
(and )Tj
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(one )Tj
8.6576 0 0 7.9001 282.17 341.29 Tm
(in )Tj
8.4787 0 0 7.9001 295.84 341.29 Tm
(column )Tj
9.1298 0 0 7.9001 227.5 326.89 Tm
(vertex )Tj
8.9729 0 0 7.9001 258.57 326.89 Tm
(of )Tj
8.5902 0 0 7.9001 272.62 326.89 Tm
(column )Tj
8.9581 0 0 7.9001 306.63 326.89 Tm
(C. )Tj
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(1 )Tj
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(J-)Tj
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(of )Tj
8.2555 0 0 7.9001 241.66 312.85 Tm
(column )Tj
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(C. )Tj
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(1 )Tj
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(not )Tj
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(in )Tj
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(J+ )Tj
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(Hi )Tj
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(lying )Tj
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(in )Tj
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(any )Tj
8.8113 0 0 7.9001 86.39 298.81 Tm
(row )Tj
8.2739 0 0 7.9001 106.75 298.81 Tm
(below )Tj
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(x. )Tj
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(Note )Tj
9.5218 0 0 7.9001 175.66 298.99 Tm
(that )Tj
8.4697 0 0 7.9001 197.26 298.99 Tm
(the )Tj
8.8709 0 0 7.9001 214.18 298.63 Tm
(vertices )Tj
8.5556 0 0 7.9001 251.02 298.63 Tm
(of )Tj
8.7675 0 0 7.9001 264.51 298.63 Tm
(C. )Tj
0 Tc 7.7 0 0 7.7 278.55 298.63 Tm
(1 )Tj
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(and )Tj
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(C. )Tj
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(1 )Tj
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(J-)Tj
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0.0139 Tc 7.1 0 0 7.1 312.25 293.77 Tm
(J+ )Tj
/T1_0 1 Tf
0.05 Tc 8.5172 0 0 7.9001 16.73 285.13 Tm
(not )Tj
8.4583 0 0 7.9001 34.76 285.13 Tm
(joined )Tj
9.1676 0 0 7.9001 63.7 285.13 Tm
(to )Tj
0 Tc 7.9001 0 0 7.9001 77.01 285.13 Tm
(x )Tj
0.05 Tc 8.8629 0 0 7.9001 88.1 285.13 Tm
(form )Tj
8.4272 0 0 7.9001 122.68 285.13 Tm
(clique )Tj
8.4356 0 0 7.9001 151.31 285.13 Tm
(in )Tj
/T1_2 1 Tf
0 Tc 7.1 0 0 7.1 164.05 285.13 Tm
(G)Tj
0.05 Tc 6.4317 0 0 5.6 169.71 280.45 Tm
(Zt )Tj
/T1_0 1 Tf
8.7642 0 0 7.9001 181.36 285.13 Tm
(of )Tj
8.4807 0 0 7.9001 195 285.13 Tm
(size )Tj
8.8194 0 0 7.9001 215.09 285.13 Tm
(r. )Tj
-0.0115 Tc 7.9001 0 0 7.9001 233.09 285.13 Tm
(As )Tj
0 Tc 1.889 0 Td
(x )Tj
0.05 Tc 8.4876 0 0 7.9001 258.59 285.13 Tm
(is )Tj
9.3488 0 0 7.9001 270.45 285.13 Tm
(an )Tj
9.7337 0 0 7.9001 285.92 285.13 Tm
(arbitrary )Tj
8.8671 0 0 7.9001 16.72 271.09 Tm
(vertex )Tj
9.1816 0 0 7.9001 47.61 271.09 Tm
(of )Tj
0 Tc 7.2 0 0 7.2 62.75 271.09 Tm
(G )Tj
0.05 Tc 8.6242 0 0 7.9001 82.25 271.09 Tm
(we )Tj
8.5952 0 0 7.9001 99.64 271.09 Tm
(can )Tj
8.3691 0 0 7.9001 119.44 271.09 Tm
(conclude )Tj
9.3029 0 0 7.9001 159.64 271.09 Tm
(that )Tj
0 Tc 7.2 0 0 7.2 181.91 271.09 Tm
(G )Tj
0.05 Tc 8.6601 0 0 7.9001 214.1 271.09 Tm
(\(2r )Tj
8.0607 0 0 8 68.72 266.41 Tm
(zt )Tj
6.6181 0 0 6.3001 187.72 266.41 Tm
(Zt )Tj
9.3731 0 0 7.9001 243.11 271.27 Tm
(I\)-regular )Tj
8.5774 0 0 7.9001 290.43 271.27 Tm
(and )Tj
9.2893 0 0 7.9001 311.02 271.27 Tm
(the )Tj
8.5297 0 0 7.9001 16.73 257.05 Tm
(non-neighbours )Tj
9.3902 0 0 7.9001 81.09 257.05 Tm
(of )Tj
8.3424 0 0 7.9001 94.42 257.05 Tm
(any )Tj
9.0641 0 0 7.9001 111.94 257.05 Tm
(vertex )Tj
8.9481 0 0 7.9001 141.56 257.05 Tm
(form )Tj
0 Tc 7.9001 0 0 7.9001 165.16 257.05 Tm
(a )Tj
0.05 Tc 8.3598 0 0 7.9001 173.8 257.05 Tm
(clique )Tj
8.5556 0 0 7.9001 200.8 257.05 Tm
(of )Tj
8.4807 0 0 7.9001 213.36 257.05 Tm
(size )Tj
9.1039 0 0 8.3 232.73 257.05 Tm
(r. )Tj
0.0305 Tc 7.9001 0 0 7.9001 42.52 229.15 Tm
(Now )Tj
0.05 Tc 8.4755 0 0 7.9001 64.61 229.15 Tm
(we )Tj
8.6146 0 0 7.9001 81.42 229.15 Tm
(show )Tj
9.5218 0 0 7.9001 106.9 229.15 Tm
(that )Tj
/T1_2 1 Tf
9.4456 0 0 7.3001 128.79 229.15 Tm
(d\(G)Tj
6.8215 0 0 5.6 145.76 224.29 Tm
(Zt)Tj
0 Tc 5.6 0 0 5.6 153.08 229.15 Tm
(\) )Tj
-0.035 Tc 3.6253 0 0 5.6 161.37 229.15 Tm
(::::; )Tj
/T1_0 1 Tf
0.05 Tc 8.5349 0 0 7.9001 172.07 229.15 Tm
(r. )Tj
8.5065 0 0 7.9001 190.39 229.15 Tm
(Let )Tj
0 Tc 7.4001 0 0 7.4001 208.55 229.15 Tm
(Q )Tj
0.05 Tc 8.2368 0 0 7.9001 219.61 229.15 Tm
(be )Tj
9.1527 0 0 7.9001 233.8 229.15 Tm
(the )Tj
9.3459 0 0 7.9001 252.64 229.15 Tm
(largest )Tj
8.6294 0 0 7.9001 286.66 229.15 Tm
(clique )Tj
8.4356 0 0 7.9001 316.55 229.15 Tm
(in )Tj
8.4138 0 0 7.9001 42.03 214.93 Tm
(Consider )Tj
0 Tc 7.9001 0 0 7.9001 81.46 214.93 Tm
(a )Tj
0.05 Tc 8.9327 0 0 7.9001 91.96 214.93 Tm
(vertex )Tj
0 Tc 7.9001 0 0 7.9001 122.19 214.93 Tm
(x )Tj
0.05 Tc 8.5426 0 0 7.9001 132.54 214.93 Tm
(say, )Tj
8.725 0 0 7.9001 153.82 214.93 Tm
(occurring )Tj
7.9917 0 0 7.9001 196.31 214.93 Tm
(in )Tj
8.8795 0 0 7.9001 208.24 214.93 Tm
(the )Tj
8.881 0 0 7.9001 225.71 214.93 Tm
(highest )Tj
8.564 0 0 7.9001 259.55 214.93 Tm
(row. )Tj
8.4231 0 0 7.9001 289.11 214.93 Tm
(Suppose, )Tj
0 Tc 7.6 0 0 7.6 16.66 215.11 Tm
[(G )-652(. )]TJ
/T1_2 1 Tf
0.05 Tc 6.6266 0 0 5.6 22.11 210.43 Tm
(Zt )Tj
/T1_0 1 Tf
8.6545 0 0 7.9001 16.73 200.89 Tm
(without )Tj
8.4599 0 0 7.9001 51.75 200.89 Tm
(any )Tj
8.8416 0 0 7.9001 71.39 200.89 Tm
(loss )Tj
8.9729 0 0 7.9001 92.79 200.89 Tm
(of )Tj
8.9019 0 0 7.9001 106.67 200.89 Tm
(generality )Tj
9.6313 0 0 7.9001 152.26 200.89 Tm
(that )Tj
0 Tc 7.9001 0 0 7.9001 174.03 200.89 Tm
(x )Tj
/T1_2 1 Tf
5.6 0 0 5.6 184.55 200.89 Tm
(E )Tj
/T1_0 1 Tf
-0.0091 Tc 7.9001 0 0 7.9001 195.04 200.89 Tm
(C!' )Tj
0.05 Tc 8.3424 0 0 7.9001 16.66 186.67 Tm
(any )Tj
8.9327 0 0 7.9001 34.54 186.67 Tm
(vertex )Tj
8.9729 0 0 7.9001 64.17 186.67 Tm
(of )Tj
/T1_2 1 Tf
0 Tc 7.1 0 0 7.1 77.48 186.67 Tm
(C )Tj
/T1_0 1 Tf
6.2 0 0 6.2 83.13 186.67 Tm
(2 )Tj
0.05 Tc 8.3695 0 0 7.9001 91.45 186.67 Tm
(belonging )Tj
8.9493 0 0 7.9001 133.18 186.67 Tm
(to )Tj
8.5774 0 0 7.9001 145.89 186.67 Tm
(any )Tj
8.485 0 0 7.9001 164.15 186.67 Tm
(row )Tj
8.2055 0 0 7.9001 183.43 186.67 Tm
(below )Tj
8.3793 0 0 7.9001 216.75 200.89 Tm
(Since )Tj
0 Tc 7.9001 0 0 7.9001 242.97 200.89 Tm
(x )Tj
0.05 Tc 8.4876 0 0 7.9001 254.09 200.89 Tm
(is )Tj
9.0413 0 0 7.9001 266.39 200.89 Tm
(not )Tj
8.8517 0 0 7.9001 285.51 200.89 Tm
(joined )Tj
8.9493 0 0 7.9001 316.06 200.89 Tm
(to )Tj
9.0161 0 0 7.9001 209.68 186.85 Tm
(the )Tj
8.8113 0 0 7.9001 226.79 186.85 Tm
(row )Tj
8.6576 0 0 7.9001 246.71 186.85 Tm
(in )Tj
8.5989 0 0 7.9001 259.01 186.85 Tm
(which )Tj
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(x )Tj
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(is, )Tj
9.1527 0 0 7.9001 311.56 186.85 Tm
(the )Tj
8.7665 0 0 7.9001 16.72 172.63 Tm
(vertices )Tj
9.1816 0 0 7.9001 52.47 172.63 Tm
(of )Tj
0 Tc 7.4001 0 0 7.4001 66.35 172.63 Tm
(Q )Tj
0.05 Tc 10.0463 0 0 7.9001 77.12 172.63 Tm
(are )Tj
8.656 0 0 7.9001 96.04 172.63 Tm
(contained )Tj
8.4356 0 0 7.9001 138.89 172.63 Tm
(in )Tj
8.1998 0 0 7.9001 151.48 172.63 Tm
(columns )Tj
0 Tc 7.9001 0 0 7.9001 187.48 172.63 Tm
(C)Tj
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5.5001 0 0 5.5001 192.79 167.95 Tm
(1 )Tj
/T1_0 1 Tf
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(and )Tj
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(C)Tj
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5.5001 0 0 5.5001 224.22 167.95 Tm
(3)Tj
0.751 0.851 Td
(' )Tj
/T1_0 1 Tf
0.05 Tc 7.9255 0 0 7.9001 241.78 172.63 Tm
(Now )Tj
8.7885 0 0 7.9001 263.44 172.63 Tm
(observing )Tj
9.8502 0 0 7.9001 307.24 172.63 Tm
(that )Tj
7.9917 0 0 7.9001 17.03 158.41 Tm
(in )Tj
8.3424 0 0 7.9001 29.8 158.41 Tm
(any )Tj
0.0275 Tc 7.8001 0 0 7.8001 48.57 158.41 Tm
(Hi )Tj
0 Tc 7.9001 0 0 7.9001 62.92 158.41 Tm
(a )Tj
0.05 Tc 9.3268 0 0 7.9001 73.6 158.41 Tm
(vertex )Tj
8.9729 0 0 7.9001 105.21 158.41 Tm
(of )Tj
0 Tc 7.9001 0 0 7.9001 119.44 158.41 Tm
(C)Tj
6 0 0 6 124.53 153.55 Tm
(1 )Tj
0.05 Tc 8.7448 0 0 7.9001 133.49 158.41 Tm
(is )Tj
8.655 0 0 7.9001 146.36 158.41 Tm
(joined )Tj
9.1676 0 0 7.9001 175.66 158.41 Tm
(to )Tj
7.9304 0 0 7.9001 189.46 158.41 Tm
(only )Tj
8.0389 0 0 7.9001 211.06 158.41 Tm
(one )Tj
9.1955 0 0 7.9001 229.66 158.41 Tm
(vertex )Tj
8.9729 0 0 7.9001 260.91 158.41 Tm
(of )Tj
0 Tc 7.8001 0 0 7.8001 275.14 158.41 Tm
(C)Tj
6 0 0 6 280.73 153.73 Tm
(3)Tj
0.717 0.78 Td
(, )Tj
0.05 Tc 8.6242 0 0 7.9001 293.57 158.41 Tm
(we )Tj
8.8408 0 0 7.9001 310.59 158.41 Tm
(can )Tj
8.1404 0 0 7.9001 17.02 144.55 Tm
(conclude )Tj
9.7407 0 0 7.9001 53.98 144.55 Tm
(that )Tj
0 Tc 7.6 0 0 7.6 75.16 144.55 Tm
(Q )Tj
0.05 Tc 8.949 0 0 7.9001 85.13 144.55 Tm
(has )Tj
8.6954 0 0 7.9001 102.84 144.55 Tm
(size )Tj
9.1039 0 0 7.9001 122.57 144.55 Tm
(r. )Tj
8.578 0 0 7.9001 138.35 144.55 Tm
(This )Tj
8.4129 0 0 7.9001 159.76 144.55 Tm
(completes )Tj
8.8795 0 0 7.9001 201.76 144.55 Tm
(the )Tj
8.8588 0 0 7.9001 218.17 144.55 Tm
(proof )Tj
9.3902 0 0 7.9001 243.81 144.55 Tm
(of )Tj
8.8795 0 0 7.9001 256.84 144.55 Tm
(the )Tj
8.4892 0 0 7.9001 273.71 144.55 Tm
(lemma. )Tj
/T1_2 1 Tf
0 Tc 5 0 0 5 311.52 144.55 Tm
(0 )Tj
/T1_0 1 Tf
-0.035 Tc 7.6321 0 0 7.9001 42.63 116.46 Tm
(We )Tj
0.05 Tc 8.9638 0 0 7.9001 58.23 116.46 Tm
(consider )Tj
8.1157 0 0 7.9001 97.01 116.46 Tm
(now )Tj
9.1527 0 0 7.9001 116.8 116.46 Tm
(the )Tj
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