论文信息 - Counting 1-Factors in Regular Bipartite Graphs

Counting 1-Factors in Regular Bipartite Graphs

We show that anyk-regular bipartite graph with 2nvertices has at least(k?1)k-1kk-2nperfect matchings (1-factors). Equivalently, this is a lower bound on the permanent of any nonnegative integern×nmatrix with each row and column sum equal tok. For anyk, the base (k?1)k?1/kk?2is largest possible.

Alexander Schrijver | A. Schrijver

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