Rainbow matchings for 3-uniform hypergraphs

Abstract

Kühn, Osthus, and Treglown and, independently, Khan proved that if H is a 3-uniform hypergraph with n vertices, where n∈3Z and large, and δ1(H)>(n−12)−(2n/32), then H contains a perfect matching. In this paper, we show that for n∈3Z sufficiently large, if F1,…,Fn/3 are 3-uniform hypergraphs with a common vertex set and δ1(Fi)>(n−12)−(2n/32) for i∈[n/3], then {F1,…,Fn/3} admits a rainbow matching, i.e., a matching consisting of one edge from each Fi. This is done by converting the rainbow matching problem to a perfect matching problem in a special class of uniform hypergraphs.