Abstract
Abstract In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number and the harmonious chromatic number of P 4 -tidy graphs and ( q , q − 4 )-graphs, for every fixed q. These classes include cographs, P 4 -sparse and P 4 -lite graphs. We also obtain a polynomial time algorithm to determine the Grundy number of ( q , q − 4 )-graphs. All these coloring problems are known to be NP-hard for general graphs.
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