Star clusters in independence complexes of graphs

  • Barmak J
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Abstract

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.

Author-supplied keywords

  • Graphs
  • Homotopy invariants
  • Homotopy types
  • Independence complexes
  • Simplicial complexes

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