Perfect matching in 3-uniform hypergraphs with large vertex degree
Abstract
A perfect matching in a 3-uniform hypergraph on n=3k vertices is a subset of n3 disjoint edges. We prove that if H is a 3-uniform hypergraph on n=3k vertices such that every vertex belongs to at least n-1 2 - 2n/3 2+1 edges then H contains a perfect matching. We give a construction to show that this result is best possible.
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