b-Coloring Parameterized by Clique-Width

Authors Lars Jaffke, Paloma T. Lima, Daniel Lokshtanov

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Lars Jaffke
  • University of Bergen, Norway
Paloma T. Lima
  • University of Bergen, Norway
Daniel Lokshtanov
  • University of California Santa Barbara, CA, USA

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Lars Jaffke, Paloma T. Lima, and Daniel Lokshtanov. b-Coloring Parameterized by Clique-Width. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial-time results on graph classes, and answers open questions posed by Campos and Silva [Algorithmica, 2018] and Bonomo et al. [Graphs Combin., 2009]. This constitutes the first result concerning structural parameterizations of this problem. We show that the problem is FPT when parameterized by the vertex cover number on general graphs, and on chordal graphs when parameterized by the number of colors. Additionally, we observe that our algorithm for graphs of bounded clique-width can be adapted to solve the Fall Coloring problem within the same runtime bound. The running times of the clique-width based algorithms for b-Coloring and Fall Coloring are tight under the Exponential Time Hypothesis.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph coloring
  • b-Coloring
  • clique-width
  • vertex cover
  • structural parameterization


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