A superlinear bound on the number of perfect matchings in cubic bridgeless graphs

TL;DR

This paper proves the first superlinear lower bound on the number of perfect matchings in cubic bridgeless graphs, advancing understanding beyond previously known linear bounds.

Contribution

It establishes the first superlinear bound on perfect matchings in cubic bridgeless graphs, extending the known results beyond bipartite and planar cases.

Findings

First superlinear bound proved for general cubic bridgeless graphs

Advances the understanding of perfect matchings in complex graph classes

Provides new insights into Lovasz and Plummer's conjecture

Abstract

Lovasz and Plummer conjectured in the 1970's that cubic bridgeless graphs have exponentially many perfect matchings. This conjecture has been verified for bipartite graphs by Voorhoeve in 1979, and for planar graphs by Chudnovsky and Seymour in 2008, but in general only linear bounds are known. In this paper, we provide the first superlinear bound in the general case.