Exact minimum codegree threshold for K-4-factors

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Colleges, School and Institutes


Given hypergraphs F and H, an F-factor in H is a set of vertex-disjoint copies of F which cover all the vertices in H. Let K 4 denote the 3-uniform hypergraph with four vertices and three edges. We show that for sufficiently large n ∈ 4ℕ, every 3-uniform hypergraph H on n vertices with minimum codegree at least n/2−1 contains a K 4-factor. Our bound on the minimum codegree here is best possible. It resolves a conjecture of Lo and Markström [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.


Original languageEnglish
Pages (from-to)856-885
JournalCombinatorics, Probability and Computing
Publication statusPublished - 4 Aug 2017


  • math.CO, 05C35, 05C65, 05C70, primary 05C70, secondary 05C35, 05C65