Counting 1-factors in regular bipartite graphs

Abstract

We show that any k-regular bipartite graph with In vertices has at least ((k-1)k-1/kk-2)n perfect matchings (1-factors). Equivalently, this is a lower bound on the permanent of any nonnegative integer n×n matrix with each row and column sum equal to k. For any k, the base (k-1)k-1/kk-2 is largest possible. © 1998 Academic Press.