We determine the minimum vertex degree that ensures a perfect matching in a
3-uniform hypergraph. More precisely, suppose that H is a sufficiently large
3-uniform hypergraph whose order n is divisible by 3. If the minimum vertex
degree of H is greater than \binom{n-1}{2}-\binom{2n/3}{2}, then H contains a
perfect matching. This bound is tight and answers a question of Han, Person and
Schacht. More generally, we show that H contains a matching of size d\le n/3 if
its minimum vertex degree is greater than \binom{n-1}{2}-\binom{n-d}{2}, which
is also best possible. This extends a result of Bollobas, Daykin and Erdos.Comment: 18 pages, 1 figure. To appear in JCT
