2026-08-06T07:03:45Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18724 2024-03-06T11:02:34Z ddc:004 open_access

Coloring Tournaments with Few Colors: Algorithms and Complexity Klingelhoefer, Felix Newman, Alantha Tournaments Graph Coloring Algorithms Complexity 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Felix Klingelhoefer and Alantha Newman 2023 Is Part Of LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2023.71 urn:nbn:de:0030-drops-187247 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.71 eng https://creativecommons.org/licenses/by/4.0/legalcode