b-coloring graphs with large girth
Combinatorics
2012-02-21 v1
Abstract
A b-coloring of a graph is a coloring of its vertices such that every color class contains a vertex that has a neighbor in all other classes. The b-chromatic number of a graph is the largest integer k such that the graph has a b-coloring with k colors. We show how to compute in polynomial time the b-chromatic number of a graph of girth at least 9. This improves the seminal result of Irving and Manlove on trees.
Cite
@article{arxiv.1202.4032,
title = {b-coloring graphs with large girth},
author = {Victor Campos and Victor Farias and Ana Silva},
journal= {arXiv preprint arXiv:1202.4032},
year = {2012}
}