Perfect matchings in 4-uniform hypergraphs

A perfect matching in a 4-uniform hypergraph on n vertices is a subset of ? n 4 ? disjoint edges. We prove that if H is a sufficiently large 4-uniform hypergraph on n = 4 k vertices such that every vertex belongs to more than ( n - 1 3 ) - ( 3 n / 4 3 ) edges, then H contains a perfect matching. A construction due to Han, Person, and Schacht shows that this result is the best possible.

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