Perfect matchings in 4-uniform hypergraphs

Abstract

A perfect matching in a 4-uniform hypergraph on n vertices is a subset of ⌊n4⌋ disjoint edges. We prove that if H is a sufficiently large 4-uniform hypergraph on n=4k vertices such that every vertex belongs to more than (n−13)−(3n/43) edges, then H contains a perfect matching. A construction due to Hàn, Person, and Schacht shows that this result is the best possible.