A characterization of b-perfect graphs
Discrete Mathematics
2012-12-13 v1
Abstract
A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b-chromatic number of a graph is the largest integer such that admits a b-coloring with colors. A graph is b-perfect if the b-chromatic number is equal to the chromatic number for every induced subgraph of . We prove that a graph is b-perfect if and only if it does not contain as an induced subgraph a member of a certain list of twenty-two graphs. This entails the existence of a polynomial-time recognition algorithm and of a polynomial-time algorithm for coloring exactly the vertices of every b-perfect graph.
Cite
@article{arxiv.1004.5306,
title = {A characterization of b-perfect graphs},
author = {Chinh T. Hoàng and Frédéric Maffray and Meriem Mechebbek},
journal= {arXiv preprint arXiv:1004.5306},
year = {2012}
}