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/
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### Colouring Polygon Visibility Graphs and Their Generalizations

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### 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},
}`