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arXiv · 1012.2878

Exponentially many perfect matchings in cubic graphs

Louis Esperet·Frantisek Kardos·Andrew King·Daniel Kral·Serguei Norine
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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.

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Louis Esperet, Frantisek Kardos, Andrew King, Daniel Kral, Serguei Norine. 2011-09-05. Exponentially many perfect matchings in cubic graphs. https://doi.org/10.1016/j.aim.2011.03.015

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