Rainbow matchings for 3-uniform hypergraphs

[摘要] Kuhn, Osthus, and Treglown and, independently, Khan proved that if His a 3-uniform hypergraph with n vertices, where n epsilon 3Z and large, and delta(1)(H) > (n-1/2) - (2n/3/2), then H contains a perfect matching. In this paper, we show that for n epsilon 3Z sufficiently large, if F-1, . . . , F-n/3 are 3-uniform hypergraphs with a common vertex set and delta(1)(F-i) > (n-1/2) - (2n/3/2) for i epsilon [n/3], then {F-1, . . . , F-n/3} admits a rainbow matching, i.e., a matching consisting of one edge from each F-i. This is done by converting the rainbow matching problem to a perfect matching problem in a special class of uniform hypergraphs. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-01

[关键词] 3-graph;Rainbow matching;Perfect matching;Fractional matching