License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2023.71
URN: urn:nbn:de:0030-drops-187247
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18724/
Klingelhoefer, Felix ;
Newman, Alantha
Coloring Tournaments with Few Colors: Algorithms and Complexity
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.
BibTeX - Entry
@InProceedings{klingelhoefer_et_al:LIPIcs.ESA.2023.71,
author = {Klingelhoefer, Felix and Newman, Alantha},
title = {{Coloring Tournaments with Few Colors: Algorithms and Complexity}},
booktitle = {31st Annual European Symposium on Algorithms (ESA 2023)},
pages = {71:1--71:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-295-2},
ISSN = {1868-8969},
year = {2023},
volume = {274},
editor = {G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18724},
URN = {urn:nbn:de:0030-drops-187247},
doi = {10.4230/LIPIcs.ESA.2023.71},
annote = {Keywords: Tournaments, Graph Coloring, Algorithms, Complexity}
}
Keywords: |
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Tournaments, Graph Coloring, Algorithms, Complexity |
Collection: |
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31st Annual European Symposium on Algorithms (ESA 2023) |
Issue Date: |
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2023 |
Date of publication: |
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30.08.2023 |