Independence complexes of claw-free graphs
组合数学
2007-05-23 v1
摘要
We study the class of independence complexes of claw-free graphs. The main theorem give good bounds on the connectivity of these complexes, given bounds for a few subcomplexes of the same class. Two applications are presented. Firstly, we show that the independence complex of a claw-free graph with n vertices and maximal degree d is (cn/d+epsilon)-connected, where c=2/3. This can be compared with the result of Szabo and Tardos that c=1/2 is optimal with no restrictions on the graphs. Secondly, we calculate the connectivity of a family of complexes used in Babson and Kozlov's proof of Lovasz conjecture.
引用
@article{arxiv.math/0512420,
title = {Independence complexes of claw-free graphs},
author = {Alexander Engström},
journal= {arXiv preprint arXiv:math/0512420},
year = {2007}
}
备注
8 pages, 1 figure