Exponentially many perfect matchings in cubic graphs
Louis Esperet, Frantisek Kardos, Andrew King, Daniel Kral and, Serguei Norine
TL;DR
This paper proves that every cubic bridgeless graph has exponentially many perfect matchings, confirming a longstanding conjecture and providing a simplified proof with a new definition of a burl.
Contribution
It establishes a lower bound on the number of perfect matchings in cubic bridgeless graphs, confirming Lovasz and Plummer's conjecture with a new, simplified approach.
Findings
Every cubic bridgeless graph has at least 2^(|V(G)|/3656) perfect matchings.
The paper introduces a new definition of a burl.
A simplified proof of the main theorem is provided.
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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