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Journal Articles European Journal of Combinatorics Year : 2012

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

Abstract

Lovász 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.
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Dates and versions

hal-00635917 , version 1 (08-11-2011)

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Louis Esperet, František Kardoš, Daniel Kráľ. A superlinear bound on the number of perfect matchings in cubic bridgeless graphs. European Journal of Combinatorics, 2012, 33 (5), pp.767-798. ⟨10.1016/j.ejc.2011.09.027⟩. ⟨hal-00635917⟩
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