{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T18:08:02Z","timestamp":1777745282488,"version":"3.51.4"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5-6","license":[{"start":{"date-parts":[[2003,12,3]],"date-time":"2003-12-03T00:00:00Z","timestamp":1070409600000},"content-version":"unspecified","delay-in-days":32,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2003,11]]},"abstract":"<jats:p>Given a positive integer <jats:italic>n<\/jats:italic> and a family <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline1.png\"\/> of graphs, let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline2.png\"\/> denote the maximum number of colours in an edge-colouring of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline3.png\"\/> such that no subgraph of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline3.png\"\/> belonging to <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline1.png\"\/> has distinct colours on its edges. Erd\u00f6s, Simonovits and S\u00f3s [6] conjectured for fixed <jats:italic>k<\/jats:italic> with <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline4.png\"\/> that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline5.png\"\/>. This has been proved for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline6.png\"\/>. For general <jats:italic>k<\/jats:italic>, in this paper we improve the previous bound of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline7.png\"\/> to <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline8.png\"\/>. For even <jats:italic>k<\/jats:italic>, we further improve it to <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline9.png\"\/>. We also prove that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S096354830300590X_inline10.png\"\/>, which is sharp.<\/jats:p>","DOI":"10.1017\/s096354830300590x","type":"journal-article","created":{"date-parts":[[2003,12,3]],"date-time":"2003-12-03T14:23:14Z","timestamp":1070461394000},"page":"585-598","source":"Crossref","is-referenced-by-count":45,"title":["On the Erd\u0151s\u2013Simonovits\u2013S\u00f3s Conjecture about the Anti-Ramsey Number of a Cycle"],"prefix":"10.1017","volume":"12","author":[{"given":"T","family":"Jiang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D","family":"West","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2003,12,3]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354830300590X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T09:22:56Z","timestamp":1589534576000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354830300590X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,11]]},"references-count":0,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2003,11]]}},"alternative-id":["S096354830300590X"],"URL":"https:\/\/doi.org\/10.1017\/s096354830300590x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,11]]}}}