Shedding vertices of vertex decomposable graphs
Combinatorics
2018-08-29 v2 Commutative Algebra
Abstract
We focus our attention on well-covered graphs that are vertex decomposable. We show that for many known families of these vertex decomposable graphs, the set of shedding vertices forms a dominating set. We then construct three new infinite families of well-covered graphs, none of which have this property. We use these results to provide a minimal counterexample to a conjecture of Villarreal regarding Cohen-Macaulay graphs.
Cite
@article{arxiv.1606.04447,
title = {Shedding vertices of vertex decomposable graphs},
author = {Jonathan Baker and Kevin N. Vander Meulen and Adam Van Tuyl},
journal= {arXiv preprint arXiv:1606.04447},
year = {2018}
}
Comments
23 pages; the content of the paper has been re-organized. This version will appear in Discrete Mathematics