Structural Parameterizations of Clique Coloring

Authors Lars Jaffke , Paloma T. Lima, Geevarghese Philip

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Author Details

Lars Jaffke
  • University of Bergen, Norway
Paloma T. Lima
  • University of Bergen, Norway
Geevarghese Philip
  • Chennai Mathematical Institute, India
  • UMI ReLaX, Chennai, India


The work was partially done while L. J. and P. T. L. were visiting Chennai Mathematical Institute.

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Lars Jaffke, Paloma T. Lima, and Geevarghese Philip. Structural Parameterizations of Clique Coloring. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 49:1-49:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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 q colors. For fixed q ≥ 2, we give an 𝒪^⋆(q^{tw})-time algorithm when the input graph is given together with one of its tree decompositions of width tw. 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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph coloring
  • clique coloring
  • treewidth
  • clique-width
  • structural parameterization
  • Strong Exponential Time Hypothesis


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