%0 Journal Article
%T Matchings in 3-uniform hypergraphs
%A Daniela K¨¹hn
%A Deryk Osthus
%A Andrew Treglown
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1009.1298v2