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Communication Dans Un Congrès Année : 2023

Coloring Tournaments with Few Colors: Algorithms and Complexity

Résumé

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.

Dates et versions

hal-04287065 , version 1 (15-11-2023)

Identifiants

Citer

Felix Klingelhoefer, Alantha Newman. Coloring Tournaments with Few Colors: Algorithms and Complexity. European Symposium on Algorithms, Sep 2023, Amsterdam (Pays-Bas), Netherlands. ⟨10.4230/LIPIcs.ESA.2023.71⟩. ⟨hal-04287065⟩

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