Pure simplicial complexes and well-covered graphs

Rashid Zaare-Nahandi

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arXiv · 1104.4556

Pure simplicial complexes and well-covered graphs

Rashid Zaare-Nahandi

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Abstract

A graph $G$ is called well-covered if all maximal independent sets of vertices have the same cardinality. A simplicial complex $\Delta$ is called pure if all of its facets have the same cardinality. Let $\mathcal G$ be the class of graphs with some disjoint maximal cliques covering all vertices. In this paper, we prove that for any simplicial complex or any graph, there is a corresponding graph in class $\mathcal G$ with the same well-coveredness property. Then some necessary and sufficient conditions are presented to recognize fast when a graph in the class $\cal G$ is well-covered or not. To do this characterization, we use an algebraic interpretation according to zero-divisor elements of the edge rings of graphs.

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Rashid Zaare-Nahandi. 2011-04-23. Pure simplicial complexes and well-covered graphs. https://arxiv.org/abs/1104.4556

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