On Perfect Matchings in Uniform Hypergraphs with Large Minimum Vertex Degree

We study sufficient -degree (1<k) conditions for the appearance of perfect and nearly perfect matchings in k-uniform hypergraphs. In particular, we obtain a minimum vertex degree condition (=1) for 3-uniform hypergraphs, which is approximately tight, by showing that every 3-uniform hypergraph on n vertices with minimum vertex degree at least (5/9+o (1) ) n2 contains a perfect matching.