# Exponentially many perfect matchings in cubic graphs

@article{Esperet2011ExponentiallyMP,
title={Exponentially many perfect matchings in cubic graphs},
author={Louis Esperet and Frantisek Kardos and Andrew D. King and Daniel Kr{\'a}l and Serguei Norine},
year={2011},
volume={227},
pages={1646-1664}
}
• Published 13 December 2010
• Mathematics
48 Citations

## Figures from this paper

A bound on the number of perfect matchings in Klee-graphs
• Mathematics
Discret. Math. Theor. Comput. Sci.
• 2013
It is shown that every Klee-graph with n ≥8 vertices has at least 3 *2(n+12)/60 perfect matchings, which is close to the bound of Esperet et al. (2011).
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Fullerene graphs have exponentially many perfect matchings
• Mathematics
• 2009
A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.
Explicit construction of regular graphs without small cycles
For every integerd>2 we give an explicit construction of infinitely many Cayley graphsX of degreed withn(X) vertices and girth >0.4801...(logn(X))/log (d−1)−2. This improves a result of Margulis.
A bound on the number of perfect matchings in Klee-graphs
• Mathematics
Discret. Math. Theor. Comput. Sci.
• 2013
It is shown that every Klee-graph with n ≥8 vertices has at least 3 *2(n+12)/60 perfect matchings, which is close to the bound of Esperet et al. (2011).
Counting 1-Factors in Regular Bipartite Graphs
We show that anyk-regular bipartite graph with 2nvertices has at least(k?1)k-1kk-2nperfect matchings (1-factors). Equivalently, this is a lower bound on the permanent of any nonnegative
Perfect matchings in planar cubic graphs
• Mathematics
Comb.
• 2012
It is proved that if G is a planar cubic graph with no cutedge, then G has at least 2-V (G), which is the number of perfect matchings in G.
Rank of maximum matchings in a graph
The problem of computing the dimension of the face of this polytope which contains the maximum cardinality matchings of a graphG is considered and a good characterization of this quantity is given, in terms of the cyclomatic number of the graph and families of odd subsets of the nodes which are always nearly perfectly matched by every maximum matching.