New bounds for the b-chromatic number of vertex deleted graphs
Combinatorics
2019-04-04 v1
Abstract
A b-coloring of a graph is a proper coloring of its vertices such that each color class contains a vertex adjacent to at least one vertex of every other color class. The b-chromatic number of a graph is the largest integer k such that the graph has a b-coloring with k colors. In this work we present lower bounds for the b-chromatic number of a vertex-deleted subgraph of a graph, particularly regarding two important classes, quasi-line and chordal graphs. We also get bounds for the b-chromatic number of G -{x}, when G is a graph with large girth.
Keywords
Cite
@article{arxiv.1904.01600,
title = {New bounds for the b-chromatic number of vertex deleted graphs},
author = {Renata Del-Vecchio and Mekkia Kouider},
journal= {arXiv preprint arXiv:1904.01600},
year = {2019}
}