Counting perfect matchings of cubic graphs in the geometric dual
Combinatorics
2010-10-29 v1
Abstract
Lov\'asz and Plummer conjectured, in the mid 1970's, that every cubic graph G with no cutedge has an exponential in |V(G)| number of perfect matchings. In this work we show that every cubic planar graph G whose geometric dual graph is a stack triangulation has at least 3 times the golden ratio to |V(G)|/72 distinct perfect matchings. Our work builds on a novel approach relating Lov\'asz and Plummer's conjecture and the number of so called groundstates of the widely studied Ising model from statistical physics.
Keywords
Cite
@article{arxiv.1010.5918,
title = {Counting perfect matchings of cubic graphs in the geometric dual},
author = {Andrea Jiménez and Marcos Kiwi},
journal= {arXiv preprint arXiv:1010.5918},
year = {2010}
}
Comments
18 pages, 8 figures