Disjoint perfect matchings in 3‐uniform hypergraphs

Abstract

AbstractFor a hypergraph H, let denote the minimum vertex degree in H. Kühn, Osthus, and Treglown proved that, for any sufficiently large integer n with , if H is a 3‐uniform hypergraph with order n and then H has a perfect matching, and this bound on is best possible. In this article, we show that under the same conditions, H contains at least pairwise disjoint perfect matchings, and this bound is sharp.