Perfect Matchings in Claw-free Cubic Graphs
Combinatorics
2022-10-05 v2
Abstract
Lovasz and Plummer conjectured that there exists a fixed positive constant c such that every cubic n-vertex graph with no cutedge has at least 2^(cn) perfect matchings. Their conjecture has been verified for bipartite graphs by Voorhoeve and planar graphs by Chudnovsky and Seymour. We prove that every claw-free cubic n-vertex graph with no cutedge has more than 2^(n/12) perfect matchings, thus verifying the conjecture for claw-free graphs.
Keywords
Cite
@article{arxiv.0906.2261,
title = {Perfect Matchings in Claw-free Cubic Graphs},
author = {Sang-il Oum},
journal= {arXiv preprint arXiv:0906.2261},
year = {2022}
}
Comments
6 pages, 2 figures