14 research outputs found
A new lower bound on the number of perfect matchings in cubic graphs
International audienceWe prove that every n-vertex cubic bridgeless graph has at least n/2 perfect matchings and give a list of all 17 such graphs that have less than n/2+2 perfect matchings
Exponentially many perfect matchings in cubic graphs
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
A superlinear bound on the number of perfect matchings in cubic bridgeless graphs
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.Comment: 54 pages v2: a short (missing) proof of Lemma 10 was adde