Exponentially many perfect matchings in cubic graphs
arXiv:1012.2878 · doi:10.1016/j.aim.2011.03.015
Abstract
We show that every cubic bridgeless graph G has at least 2^(|V(G)|/3656) perfect matchings. This confirms an old conjecture of Lovasz and Plummer. This version of the paper uses a different definition of a burl from the journal version of the paper and a different proof of Lemma 18 is given. This simplifies the exposition of our arguments throughout the whole paper.