Edge-b-coloring Trees [article]

Victor Campos, Ana Silva
2015 arXiv   pre-print
A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to at least one vertex in each other color class. The b-chromatic number of G is the maximum integer b(G) for which G has a b-coloring with b(G) colors. This problem was introduced by Irving and Manlove in 1999, where they showed that computing b(G) is NP-hard in general and polynomial-time solvable for trees. Since then, a number of complexity results were shown, including
more » ... hardness results for chordal graphs (Havet et. al., 2011) and line graphs (Campos et. al., 2015). In this article, we present a polynomial time algorithm that solves the problem restricted to claw-free block graphs, an important subclass of chordal graphs and line graphs. This is equivalent to solving the edge coloring version of the problem restricted to trees.
arXiv:1511.05422v1 fatcat:6zfkqybl7jhdldlq7axh7y6kea