Shellability, vertex decomposability, and lexicographical products of graphs
Combinatorics
2015-05-13 v1
Abstract
We investigate when the independence complex of , the lexicographical product of two graphs and , 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.
Keywords
Cite
@article{arxiv.1505.02838,
title = {Shellability, vertex decomposability, and lexicographical products of graphs},
author = {Kevin N. Vander Meulen and Adam Van Tuyl},
journal= {arXiv preprint arXiv:1505.02838},
year = {2015}
}
Comments
6 pages