Fractional and integer matchings in uniform hypergraphs

Our main result improves bounds of Markström and Ruciński on the minimum d -degree which forces a perfect matching in a k -uniform hypergraph on n vertices. We also extend bounds of Bollobás, Daykin and Erdős by asymptotically determining the minimum vertex degree which forces a matching of size t < n / 2 ( k − 1 ) in a k -uniform hypergraph on n vertices. Further asymptotically tight results on d -degrees which force large matchings are also obtained. Our approach is to prove fractional versions of the above results and then translate these into integer versions.