Star clusters in independence complexes of graphs
Combinatorics
2010-07-05 v1 Algebraic Topology
Abstract
We introduce the notion of \textit{star cluster} of a simplex in a simplicial complex. This concept provides a general tool to study the topology of independence complexes of graphs. We use star clusters to answer a question arisen from works of Engstr\"om and Jonsson on the homotopy type of independence complexes of triangle-free graphs and to investigate a large number of examples which appear in the literature. We present an alternative way to study the chromatic number of a graph from a homotopical point of view and obtain new results regarding the connectivity of independence complexes.
Cite
@article{arxiv.1007.0418,
title = {Star clusters in independence complexes of graphs},
author = {Jonathan Ariel Barmak},
journal= {arXiv preprint arXiv:1007.0418},
year = {2010}
}
Comments
22 pages, 13 figures