An Entropy Proof of the Kahn-Lovász Theorem

Abstract

Brègman gave a best possible upper bound for the number of perfect matchings in a balanced bipartite graph in terms of its degree sequence. Recently Kahn and Lovász extended Brègman's theorem to general graphs. In this paper, we use entropy methods to give a new proof of the Kahn-Lovász theorem. Our methods build on Radhakrishnan's use of entropy to prove Brègman's theorem.