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arXiv · 1505.02838

Shellability, vertex decomposability, and lexicographical products of graphs

Kevin N. Vander Meulen·Adam Van Tuyl
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Abstract

We investigate when the independence complex of $G[H]$, the lexicographical product of two graphs $G$ and $H$, is either vertex decomposable or shellable. As an application, we construct an infinite family of graphs with the property that every graph in this family has the property that the independence complex of each graph is shellable, but not vertex decomposable.

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Kevin N. Vander Meulen, Adam Van Tuyl. 2015-05-12. Shellability, vertex decomposability, and lexicographical products of graphs. https://arxiv.org/abs/1505.02838

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