Star clusters in independence complexes of graphs

Citations of this article
Mendeley users who have this article in their library.
Get full text


We introduce the notion of 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 Engström 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 and clique numbers of a graph from a homotopical point of view and obtain new results regarding the connectivity of independence complexes. © 2013 Elsevier Ltd.




Barmak, J. A. (2013). Star clusters in independence complexes of graphs. Advances in Mathematics, 241, 33–57.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free