{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T06:40:53Z","timestamp":1698043253996},"reference-count":12,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6305,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,7]]},"abstract":"Abstract<\/jats:title>A typical problem arising in Ramsey graph theory is the following. For given graphs G<\/jats:italic> and L<\/jats:italic>, how few colors can be used to color the edges of G<\/jats:italic> in order that no monochromatic subgraph isomorphic to L<\/jats:italic> is formed? In this paper we investigate the opposite extreme. That is, we will require that in any subgraph of G<\/jats:italic> isomorphic to L, all<\/jats:italic> its edges have different<\/jats:italic> colors. We call such a subgraph a totally multicolored copy of L.<\/jats:italic> Of particular interest to us will be the determination of Xs<\/jats:sub>(n, e, L<\/jats:italic>), defined to be the minimum number of colors needed to edge\u2010color some graph G<\/jats:italic>(n<\/jats:italic>, \u03f5) with n<\/jats:italic> vertices and e<\/jats:italic> edges so that all copies of L<\/jats:italic> in it are totally multicolored.<\/jats:p>It turns out that some of these questions are surprisingly deep, and are intimately related, for example, to the well\u2010studied (but little understood) functions r<\/jats:italic>k<\/jats:sub>(n<\/jats:italic>), defined to be the size of the largest subset of {1, 2,\u2026, n<\/jats:italic>} containing no k<\/jats:italic>\u2010term arithmetic progression, and g<\/jats:italic>(n; k, l<\/jats:italic>), defined to be the maximum number of triples which can be formed from {1, 2,\u2026, n<\/jats:italic>} so that no two triples share a common pair, and no k<\/jats:italic> elements of {1, 2,\u2026, n<\/jats:italic>} span l<\/jats:italic> triples.<\/jats:p>","DOI":"10.1002\/jgt.3190130302","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:27:14Z","timestamp":1180182434000},"page":"263-282","source":"Crossref","is-referenced-by-count":6,"title":["Maximal antiramsey graphs and the strong chromatic number"],"prefix":"10.1002","volume":"13","author":[{"given":"S. A.","family":"Burr","sequence":"first","affiliation":[]},{"given":"P.","family":"Erd\u00f6s","sequence":"additional","affiliation":[]},{"given":"R. L.","family":"Graham","sequence":"additional","affiliation":[]},{"given":"V.","family":"T. S\u00f3s","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"N.AlonandJ.Kahn personal communication."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.32.12.331"},{"key":"e_1_2_1_4_2","unstructured":"S.Berkowitz personal communication."},{"key":"e_1_2_1_5_2","unstructured":"S. A.Burr P.Erd\u00f6s P.Frankl R. L.GrahamandV. T.S\u00f3s to appear."},{"key":"e_1_2_1_6_2","volume-title":"Extremal Graph Theory","author":"Bollob\u00e1s B.","year":"1978"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1215\/ijm\/1255631811","article-title":"On a theorem of Rademacher\u2010Tur\u00e1n","volume":"6","author":"Erd\u00f6s P.","year":"1962","journal-title":"Illinois J. Math."},{"key":"e_1_2_1_8_2","first-page":"51","article-title":"A limit theorem in graph theory","volume":"1","author":"Erd\u00f6s P.","year":"1966","journal-title":"Stud. Sci. Math. Hungar."},{"key":"e_1_2_1_9_2","unstructured":"P.Erd\u00f6sandM.Simonovits to appear."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"e_1_2_1_11_2","first-page":"939","volume-title":"Combinatorics II","author":"Ruzsa I.","year":"1978"},{"key":"e_1_2_1_12_2","first-page":"279","volume-title":"Theory of Graphs","author":"Simonovits M.","year":"1968"},{"key":"e_1_2_1_13_2","unstructured":"E.Szemer\u00e9di Regular partitions of graphs. Colloq. Int. C.N.R.S. No. 260 Probl\u00e8mes combinatoire et th\u00e9orie des graphes (1978)399\u2013401."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130302","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130302","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T13:28:03Z","timestamp":1697981283000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,7]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1989,7]]}},"alternative-id":["10.1002\/jgt.3190130302"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130302","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,7]]}}}