{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T05:29:10Z","timestamp":1732166950053,"version":"3.28.0"},"reference-count":4,"publisher":"Wiley","license":[{"start":{"date-parts":[[2010,8,1]],"date-time":"2010-08-01T00:00:00Z","timestamp":1280620800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We determine the minimal density of triangles in a tripartite graph with prescribed edge densities. This extends a previous result of Bondy, Shen, Thomass\u00e9 and Thomassen characterizing those edge densities guaranteeing the existence of a triangle in a tripartite graph. To be precise we show that a suitably weighted copy of the graph formed by deleting a certain 9-cycle from <jats:italic>K<\/jats:italic><jats:sub>3,3,3<\/jats:sub> has minimal triangle density among all weighted tripartite graphs with prescribed edge densities.<\/jats:p><jats:p><jats:uri xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:type=\"simple\" xlink:href=\"http:\/\/journals.cambridge.org\/sup_S1461157009000436sup001\">Supplementary materials are available with this article.<\/jats:uri><\/jats:p>","DOI":"10.1112\/s1461157009000436","type":"journal-article","created":{"date-parts":[[2010,8,27]],"date-time":"2010-08-27T11:06:33Z","timestamp":1282907193000},"page":"388-413","source":"Crossref","is-referenced-by-count":2,"title":["The minimal density of triangles in tripartite graphs"],"prefix":"10.1112","volume":"13","author":[{"given":"Rahil","family":"Baber","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. Robert","family":"Johnson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Talbot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,8,1]]},"reference":[{"volume-title":"Proceedings of the Fifth British Combinatorial Conference","year":"1976","author":"Bollob\u00e1s","key":"S1461157009000436_ref1"},{"key":"S1461157009000436_ref5","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/978-3-0348-5438-2_41","volume-title":"Studies in pure mathematics","author":"Lov\u00e1sz","year":"1983"},{"key":"S1461157009000436_ref3","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1215\/ijm\/1255631811","volume":"6","author":"Erd\u0151s","year":"1962","journal-title":"Illinois J. Math."},{"key":"S1461157009000436_ref6","first-page":"60","volume":"10","author":"Mantel","year":"1907","journal-title":"Wiskundige Opgaven"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157009000436","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,20]],"date-time":"2024-11-20T13:15:33Z","timestamp":1732108533000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157009000436\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,1]]},"references-count":4,"alternative-id":["S1461157009000436"],"URL":"https:\/\/doi.org\/10.1112\/s1461157009000436","relation":{},"ISSN":["1461-1570"],"issn-type":[{"type":"electronic","value":"1461-1570"}],"subject":[],"published":{"date-parts":[[2010,8,1]]}}}