Perfect Matchings in Random r-regular, s-uniform Hypergraphs

Abstract

We show that r-regular, s-uniform hypergraphs contain a perfect matching with high probability (whp), provided The Proof is based on the application of a technique of Robinson and Wormald [7, 8]. The space of hypergraphs is partitioned into subsets according to the number of small cycles in the hypergraph. The difference in the expected number of perfect matchings between these subsets explains most of the variance of the number of perfect matchings in the space of hypergraphs, and is sufficient to prove existence (whp), using the Chebychev Inequality.