Perfect matchings (and Hamilton cycles) in hypergraphs with large degrees

We establish a new lower bound on the l -wise collective minimum degree which guarantees the existence of a perfect matching in a k -uniform hypergraph, where 1 ≤ l < k / 2 . For l = 1 , this improves a long-standing bound of Daykin and Häggkvist (1981) [5]. Our proof is a modification of the approach of Hàn et al. (2009) from [12]. ition, we fill a gap left by the results solving a similar question for the existence of Hamilton cycles.