Artículos de revistas
Star clusters in independence complexes of graphs
Barmak, Jonathan Ariel; Star clusters in independence complexes of graphs; Academic Press Inc Elsevier Science; Advances In Mathematics; 241; 3-2013; 33-57
Barmak, Jonathan Ariel
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.