Perfect Matching of 3-uniform Hypergraphs

Let F be a 3-uniform 3-partite hypergraph which has a perfect matching of graphs between each two parts. We give an equivalent condition for existence of a perfect matching in F. The maximum number of disjoint hyperedges in F is denoted by β1(F) and the minimum number of vertex covers of F is denoted by α0(F). As an another result we prove that β1(F)=α0(F). Also it is proved that if F is well-covered then there is a perfect matching in F.