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.SoCG.2021.29
URN: urn:nbn:de:0030-drops-138281
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13828/
Davies, James ;
Krawczyk, Tomasz ;
McCarty, Rose ;
Walczak, Bartosz
Colouring Polygon Visibility Graphs and Their Generalizations
Abstract
Curve pseudo-visibility graphs generalize polygon and pseudo-polygon visibility graphs and form a hereditary class of graphs. We prove that every curve pseudo-visibility graph with clique number ω has chromatic number at most 3⋅4^{ω-1}. The proof is carried through in the setting of ordered graphs; we identify two conditions satisfied by every curve pseudo-visibility graph (considered as an ordered graph) and prove that they are sufficient for the claimed bound. The proof is algorithmic: both the clique number and a colouring with the claimed number of colours can be computed in polynomial time.
BibTeX - Entry
@InProceedings{davies_et_al:LIPIcs.SoCG.2021.29,
author = {Davies, James and Krawczyk, Tomasz and McCarty, Rose and Walczak, Bartosz},
title = {{Colouring Polygon Visibility Graphs and Their Generalizations}},
booktitle = {37th International Symposium on Computational Geometry (SoCG 2021)},
pages = {29:1--29:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-184-9},
ISSN = {1868-8969},
year = {2021},
volume = {189},
editor = {Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13828},
URN = {urn:nbn:de:0030-drops-138281},
doi = {10.4230/LIPIcs.SoCG.2021.29},
annote = {Keywords: Visibility graphs, \chi-boundedness, pseudoline arrangements, ordered graphs}
}
Keywords: |
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Visibility graphs, χ-boundedness, pseudoline arrangements, ordered graphs |
Collection: |
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37th International Symposium on Computational Geometry (SoCG 2021) |
Issue Date: |
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2021 |
Date of publication: |
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02.06.2021 |