{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T05:06:32Z","timestamp":1696482392258},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2008,11,1]],"date-time":"2008-11-01T00:00:00Z","timestamp":1225497600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2008,11]]},"abstract":"<jats:p>Suppose that<jats:italic>n<\/jats:italic>&gt; (log<jats:italic>k<\/jats:italic>)<jats:sup><jats:italic>ck<\/jats:italic><\/jats:sup>, where<jats:italic>c<\/jats:italic>is a fixed positive constant. We prove that, no matter how the edges of<jats:italic>K<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>are coloured with<jats:italic>k<\/jats:italic>colours, there is a copy of<jats:italic>K<\/jats:italic><jats:sub>4<\/jats:sub>whose edges receive at most two colours. This improves the previous best bound of<jats:italic>k<\/jats:italic><jats:sup><jats:italic>c<\/jats:italic>\u2032<jats:italic>k<\/jats:italic><\/jats:sup>, where<jats:italic>c<\/jats:italic>\u2032 is a fixed positive constant, which follows from results on classical Ramsey numbers.<\/jats:p>","DOI":"10.1017\/s0963548308009413","type":"journal-article","created":{"date-parts":[[2008,10,20]],"date-time":"2008-10-20T07:15:24Z","timestamp":1224486924000},"page":"823-830","source":"Crossref","is-referenced-by-count":7,"title":["When is an Almost Monochromatic<i>K<\/i><sub>4<\/sub>Guaranteed?"],"prefix":"10.1017","volume":"17","author":[{"given":"ALEXANDR","family":"KOSTOCHKA","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DHRUV","family":"MUBAYI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,11,1]]},"reference":[{"key":"S0963548308009413_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s004930070016"},{"key":"S0963548308009413_ref2","first-page":"49","article-title":"Solved and unsolved problems in combinatorics and combinatorial number theory","volume":"32","author":"Erd\u00f6s","year":"1981","journal-title":"Congressus Numerantium"},{"key":"S0963548308009413_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-004-0019-6"},{"key":"S0963548308009413_ref4","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.1014"},{"key":"S0963548308009413_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009822"},{"key":"S0963548308009413_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01195000"},{"key":"S0963548308009413_ref7","doi-asserted-by":"crossref","first-page":"R9","DOI":"10.37236\/1553","article-title":"On edge colorings with at least q colors in every subset of p vertices","volume":"8","author":"S\u00e1rk\u00f6zy","year":"2001","journal-title":"Electron. J. Combin."},{"key":"S0963548308009413_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10129"},{"key":"S0963548308009413_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(02)00038-2"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548308009413","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,19]],"date-time":"2021-09-19T04:53:25Z","timestamp":1632027205000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548308009413\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,11]]},"references-count":9,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2008,11]]}},"alternative-id":["S0963548308009413"],"URL":"https:\/\/doi.org\/10.1017\/s0963548308009413","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,11]]}}}