Home
Scholarly Works
Shedding vertices of vertex decomposable...
Journal article

Shedding vertices of vertex decomposable well-covered graphs

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.

Authors

Baker J; Vander Meulen KN; Van Tuyl A

Journal

Discrete Mathematics, Vol. 341, No. 12, pp. 3355–3369

Publisher

Elsevier

Publication Date

December 1, 2018

DOI

10.1016/j.disc.2018.07.029

ISSN

0012-365X

Contact the Experts team