2012/02/17 by Campos, Victor, Farias, Victor, Silva, Ana
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1202.4032
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.