bb-colouring outerplanar graphs with large girth

A b-colouring of a graph is a colouring of its vertices such that every colour class contains a vertex that has a neighbour in all other classes. The b-chromatic number   of a graph is the largest integer kk such that the graph has a bb-colouring with kk colours. We show here how to compute in polynomial time the bb-chromatic number of an outerplanar graph of girth at least 88. This generalizes the seminal result of Irving and Manlove on trees.