{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T18:15:15Z","timestamp":1778955315184,"version":"3.51.4"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2002,4,25]],"date-time":"2002-04-25T00:00:00Z","timestamp":1019692800000},"content-version":"unspecified","delay-in-days":55,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2002,3]]},"abstract":"<jats:p>How large can the Lagrangian of an <jats:italic>r<\/jats:italic>-graph with <jats:italic>m<\/jats:italic> edges be? Frankl and F\u00fcredi [1] \n\nconjectured that the <jats:italic>r<\/jats:italic>-graph of size <jats:italic>m<\/jats:italic> formed by taking the first <jats:italic>m<\/jats:italic> sets in the colex \n\nordering of <jats:bold>N<\/jats:bold><jats:sup>(<jats:italic>r<\/jats:italic>)<\/jats:sup> has the largest Lagrangian of all <jats:italic>r<\/jats:italic>-graphs of size <jats:italic>m<\/jats:italic>. \n\nWe prove the first \u2018interesting\u2019 case of this conjecture, namely that the 3-graph with \n\n(<jats:sup><jats:italic>t<\/jats:italic><\/jats:sup><jats:sub>3<\/jats:sub>) edges and largest Lagrangian is [<jats:italic>t<\/jats:italic>]<jats:sup>(3)<\/jats:sup>. \n\nWe also prove that this conjecture is true for 3-graphs of several other sizes.<\/jats:p><jats:p>For general <jats:italic>r<\/jats:italic>-graphs we prove a weaker result: for <jats:italic>t<\/jats:italic> sufficiently large, the <jats:italic>r<\/jats:italic>-graph of \n\nsize (<jats:sup><jats:italic>t<\/jats:italic><\/jats:sup><jats:sub><jats:italic>r<\/jats:italic><\/jats:sub>) supported on <jats:italic>t<\/jats:italic> + 1 vertices and with largest \n\nLagrangian, is [<jats:italic>t<\/jats:italic>](<jats:sup><jats:italic>r<\/jats:italic><\/jats:sup>).<\/jats:p>","DOI":"10.1017\/s0963548301005053","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:49:03Z","timestamp":1027777743000},"page":"199-216","source":"Crossref","is-referenced-by-count":47,"title":["Lagrangians of Hypergraphs"],"prefix":"10.1017","volume":"11","author":[{"given":"J. M.","family":"TALBOT","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2002,4,25]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548301005053","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T19:53:51Z","timestamp":1554321231000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548301005053\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,3]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,3]]}},"alternative-id":["S0963548301005053"],"URL":"https:\/\/doi.org\/10.1017\/s0963548301005053","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,3]]}}}