{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T11:18:43Z","timestamp":1648552723473},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2017,8,4]],"date-time":"2017-08-04T00:00:00Z","timestamp":1501804800000},"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":[[2017,11]]},"abstract":"<jats:p>Given hypergraphs <jats:italic>F<\/jats:italic> and <jats:italic>H<\/jats:italic>, an <jats:italic>F<\/jats:italic>-factor in <jats:italic>H<\/jats:italic> is a set of vertex-disjoint copies of <jats:italic>F<\/jats:italic> which cover all the vertices in <jats:italic>H<\/jats:italic>. Let <jats:italic>K<\/jats:italic><jats:sup>\u2212<\/jats:sup><jats:sub>4<\/jats:sub> denote the 3-uniform hypergraph with four vertices and three edges. We show that for sufficiently large <jats:italic>n<\/jats:italic> \u2208 4\u2115, every 3-uniform hypergraph <jats:italic>H<\/jats:italic> on <jats:italic>n<\/jats:italic> vertices with minimum codegree at least <jats:italic>n<\/jats:italic>\/2\u22121 contains a <jats:italic>K<\/jats:italic><jats:sup>\u2212<\/jats:sup><jats:sub>4<\/jats:sub>-factor. Our bound on the minimum codegree here is best possible. It resolves a conjecture of Lo and Markstr\u00f6m [15] for large hypergraphs, who earlier proved an asymptotically exact version of this result. Our proof makes use of the absorbing method as well as a result of Keevash and Mycroft [11] concerning almost perfect matchings in hypergraphs.<\/jats:p>","DOI":"10.1017\/s0963548317000268","type":"journal-article","created":{"date-parts":[[2017,8,4]],"date-time":"2017-08-04T03:32:01Z","timestamp":1501817521000},"page":"856-885","source":"Crossref","is-referenced-by-count":5,"title":["Exact Minimum Codegree Threshold for <i>K<\/i><sup>\u2212<\/sup><sub>4<\/sub>-Factors"],"prefix":"10.1017","volume":"26","author":[{"given":"JIE","family":"HAN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ALLAN","family":"LO","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANDREW","family":"TREGLOWN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YI","family":"ZHAO","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2017,8,4]]},"reference":[{"key":"S0963548317000268_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2017.02.003"},{"key":"S0963548317000268_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548317000104"},{"key":"S0963548317000268_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700006924"},{"key":"S0963548317000268_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-014-1410-8"},{"key":"S0963548317000268_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579292"},{"key":"S0963548317000268_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-24298-9_6"},{"key":"S0963548317000268_ref8","first-page":"601","article-title":"Proof of a conjecture of Erd\u0151s","volume":"4","author":"Hajnal","year":"1970","journal-title":"Combinatorial Theory and its Applications vol. 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Minimum degree condition for C 4-tiling in 3-uniform hypergraphs. Unpublished manuscript."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548317000268","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T15:46:57Z","timestamp":1555429617000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548317000268\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,4]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2017,11]]}},"alternative-id":["S0963548317000268"],"URL":"https:\/\/doi.org\/10.1017\/s0963548317000268","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,4]]}}}