Star clusters in independence complexes of graphs |
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Authors: | Jonathan Ariel Barmak |
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Institution: | Mathematics Department, Kungliga Tekniska högskolan, Stockholm, Sweden |
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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. |
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Keywords: | 57M15 05C69 55P15 05C10 |
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