Matchings in hypergraphs

The well known marriage theorem of Hall gives a necessary and sufficient condition for the existence of a perfect matching in a bipartite graph. Unfortunately, for hypergraphs no such result is known so far. In this talk I will investigate sufficient conditions for the existence of matchings in 3-uniform hypergraphs (so we are now seeking disjoint triples of vertices instead of pairs as in the case of graphs). I will also discuss some related results on the existence of Hamilton cycles in hypergraphs.

This is joint work with Deryk Osthus