b-coloring is NP-hard on co-bipartite graphs and polytime solvable on tree-cographs

Abstract

A b-coloring of a graph is a proper coloring such that every color class contains a vertex that is adjacent to all other color classes. The b-chromatic number of a graph G, denoted by χb(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is called b-continuous if it admits a b-coloring with t colors, for every t = χ(G… (More)

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