Induced forests in some distance-regular graphs
Combinatorics
2024-04-17 v1
Abstract
In this article, we study the order and structure of the largest induced forests in some families of graphs. First we prove a variation of the ratio bound that gives an upper bound on the order of the largest induced forest in a graph. Next we define a \textsl{canonical induced forest} to be a forest that is formed by adding a vertex to a coclique and give several examples of graphs where the maximal forest is a canonical induced forest. These examples are all distance-regular graphs with the property that the Delsarte-Hoffman ratio bound for cocliques holds with equality. We conclude with some examples of related graphs where there are induced forests that are larger than a canonical forest.
Keywords
Cite
@article{arxiv.2301.05207,
title = {Induced forests in some distance-regular graphs},
author = {Karen Gunderson and Karen Meagher and Joy Morris and Venkata Raghu Tej Pantangi},
journal= {arXiv preprint arXiv:2301.05207},
year = {2024}
}