English

Structural Parameterizations of Clique Coloring

Data Structures and Algorithms 2020-05-12 v1 Computational Complexity Combinatorics

Abstract

A clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has a clique coloring with qq colors. For fixed q2q \ge 2, we give an O(qtw)\mathcal{O}^{\star}(q^{tw})-time algorithm when the input graph is given together with one of its tree decompositions of width twtw. We complement this result with a matching lower bound under the Strong Exponential Time Hypothesis. We furthermore show that (when the number of colors is unbounded) Clique Coloring is XP parameterized by clique-width.

Keywords

Cite

@article{arxiv.2005.04733,
  title  = {Structural Parameterizations of Clique Coloring},
  author = {Lars Jaffke and Paloma T. Lima and Geevarghese Philip},
  journal= {arXiv preprint arXiv:2005.04733},
  year   = {2020}
}
R2 v1 2026-06-23T15:26:20.595Z