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Minimum Codegree Threshold for C 6 3-Factors in 3-Uniform Hypergraphs

Published online by Cambridge University Press:  22 March 2017

WEI GAO  and
JIE HAN
WEI GAO
Affiliation:
Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL 36849, USA (e-mail: wzg0021@auburn.edu)
JIE HAN
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090, São Paulo, Brazil (e-mail: jhan@ime.usp.br)
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Abstract

Let C 6 3 be the 3-uniform hypergraph on {1, . . ., 6} with edges 123,345,561, which can be seen as the analogue of the triangle in 3-uniform hypergraphs. For sufficiently large n divisible by 6, we show that every n-vertex 3-uniform hypergraph H with minimum codegree at least n/3 contains a C 6 3-factor, that is, a spanning subhypergraph consisting of vertex-disjoint copies of C 6 3. The minimum codegree condition is best possible. This improves the asymptotic result obtained by Mycroft and answers a question of Rödl and Ruciński exactly.

Keywords

Primary 05C70Secondary 05C65

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 4 , July 2017 , pp. 536 - 559
Copyright
Copyright © Cambridge University Press 2017 

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