Structural Parameterizations of Clique Coloring

Abstract A clique coloring of a graph is an assignment colors to its vertices such that no maximal monochromatic. We initiate the study structural parameterizations Clique Coloring problem which asks whether given has with q colors. For fixed $$q \ge 2$$ q ≥ 2 , we give $$\mathscr {O}^{\star }(q^{{\mathsf {tw}}})$$ O ⋆ ( tw ) -time algorithm when input together one tree decompositions width $${\mathsf {tw}} $$ . complement this result matching lower bound under Strong Exponential Time Hypothesis. furthermore show (when number unbounded) $$\mathsf {XP}$$ XP parameterized by clique-width.