$$b$$ b -Coloring is NP-hard on Co-bipartite Graphs and Polytime Solvable on Tree-Cographs

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 $$G$$ G , denoted by $$\chi _b(G)$$ χ b ( G ) , is the maximum number $$t$$ t such that $$G$$ G admits a b-coloring with $$t$$ t colors. A graph  $$G$$ G is called b-continuous if it admits… CONTINUE READING