Perfect matchings in r-partite r-graphs
arXiv:0911.4008 · doi:10.1016/j.ejc.2008.02.011
Abstract
Let H be an r-partite r-graph, all of whose sides have the same size n. Suppose that there exist two sides of H, each satisfying the following condition: the degree of each legal (r-1)-tuple contained in the complement of this side is strictly larger than n/2. We prove that under this condition H must have a perfect matching. This answers a question of Kuhn and Osthus.
6 pages