Coloring Tournaments with Few Colors: Algorithms and Complexity

Authors Felix Klingelhoefer, Alantha Newman



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Author Details

Felix Klingelhoefer
  • Laboratoire G-SCOP (Univ. Grenoble Alpes), Grenoble, France
Alantha Newman
  • Laboratoire G-SCOP (CNRS, Univ. Grenoble Alpes), Grenoble, France

Acknowledgements

We thank Louis Esperet for useful discussions and for his encouragement.

Cite As Get BibTex

Felix Klingelhoefer and Alantha Newman. Coloring Tournaments with Few Colors: Algorithms and Complexity. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 71:1-71:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ESA.2023.71

Abstract

A k-coloring of a tournament is a partition of its vertices into k acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a 2-colorable tournament with few colors. This problem does not seem to have been addressed before, although it is a special case of coloring a 2-colorable 3-uniform hypergraph with few colors, which is a well-studied problem with super-constant lower bounds.
We present an efficient decomposition lemma for tournaments and show that it can be used to design polynomial-time algorithms to color various classes of tournaments with few colors, including an algorithm to color a 2-colorable tournament with ten colors. For the classes of tournaments considered, we complement our upper bounds with strengthened lower bounds, painting a comprehensive picture of the algorithmic and complexity aspects of coloring tournaments.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Approximation algorithms
Keywords
  • Tournaments
  • Graph Coloring
  • Algorithms
  • Complexity

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