A perfect matching in a 3-uniform hypergraph on $n=3k$ vertices is a subset of $\frac{ n}{ 3}$ disjoint edges. We prove that if $H$ is a 3-uniform hypergraph on $n=3k$ vertices such that every vertex belongs to at least ${ n-1\choose 2} - { 2n/3\choose 2}+1$ edges then $H$ contains a perfect matching. We give a construction to show that this result is best possible.
Categories: cs.DM math.CO