2015/09/08 by Han, Jie, Lo, Allan, Treglown, Andrew +1
#05C35 #05C65 #05C70 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1509.02577
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 4 vertices and 3 edges. We show that for sufficiently large n∈ 4 \mathbb N, 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 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 concerning almost perfect matchings in hypergraphs.