Star clusters in independence complexes of graphs
2013 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 241, 33-57 p.Article in journal (Refereed) Published
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 Engstrom 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.
Place, publisher, year, edition, pages
2013. Vol. 241, 33-57 p.
Independence complexes, Graphs, Simplicial complexes, Homotopy types, Homotopy invariants
IdentifiersURN: urn:nbn:se:kth:diva-124435DOI: 10.1016/j.aim.2013.03.016ISI: 000319367900003ScopusID: 2-s2.0-84876463099OAI: oai:DiVA.org:kth-124435DiVA: diva2:636419
FunderKnut and Alice Wallenberg Foundation
QC 201307102013-07-102013-07-052013-07-12Bibliographically approved