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Exact Minimum Codegree Threshold for K−4-Factors

Published online by Cambridge University Press:  04 August 2017

JIE HAN ,
ALLAN LO ,
ANDREW TREGLOWN  and
YI ZHAO
JIE HAN
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, SP 05508-090, Brazil (e-mail: jhan@ime.usp.br)
ALLAN LO
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK (e-mail: s.a.lo@bham.ac.uk, a.c.treglown@bham.ac.uk)
ANDREW TREGLOWN
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK (e-mail: s.a.lo@bham.ac.uk, a.c.treglown@bham.ac.uk)
YI ZHAO
Affiliation:
Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA (e-mail: yzhao6@gsu.edu)
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Abstract

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.

Keywords

Primary 05C70Secondary 05C3505C65
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 6 , November 2017 , pp. 856 - 885
Copyright
Copyright © Cambridge University Press 2017 

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