{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T02:19:52Z","timestamp":1648606792683},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2020,8,14]],"date-time":"2020-08-14T00:00:00Z","timestamp":1597363200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that any <jats:italic>n<\/jats:italic>-vertex graph whose complement is triangle-free contains <jats:italic>n<\/jats:italic><jats:sup>2<\/jats:sup>\/12 \u2013 <jats:italic>o<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>2<\/jats:sup>) edge-disjoint triangles. This is tight for the disjoint union of two cliques of order <jats:italic>n<\/jats:italic>\/2. We also prove a corresponding stability theorem, that all large graphs attaining the above bound are close to being bipartite. Our results answer a question of Alon and Linial, and make progress on a conjecture of Erd\u0151s.<\/jats:p>","DOI":"10.1017\/s096354832000036x","type":"journal-article","created":{"date-parts":[[2020,8,14]],"date-time":"2020-08-14T01:57:00Z","timestamp":1597370220000},"page":"153-162","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Many disjoint triangles in co-triangle-free graphs"],"prefix":"10.1017","volume":"30","author":[{"given":"Mykhaylo","family":"Tyomkyn","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2020,8,14]]},"reference":[{"key":"S096354832000036X_ref4","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1959.11989408"},{"key":"S096354832000036X_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548306008194"},{"key":"S096354832000036X_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(96)00044-1"},{"key":"S096354832000036X_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20031"},{"key":"S096354832000036X_ref1","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2009.170.371"},{"key":"S096354832000036X_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s004930170003"},{"key":"S096354832000036X_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(96)00044-1"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354832000036X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T11:51:22Z","timestamp":1611229882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354832000036X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,14]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["S096354832000036X"],"URL":"https:\/\/doi.org\/10.1017\/s096354832000036x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,14]]},"assertion":[{"value":"\u00a9 The Author(s), 2020. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}