b-coloring graphs with large girth

Details b-coloring graphs with large girth b-coloring graphs with large girth

2012-02-17

arxiv.org/abs/1202.4032v1

Mathematics

Combinatorics

Scientific paper

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.

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