  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.
