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Colouring Polygon Visibility Graphs and Their Generalizations

Authors James Davies, Tomasz Krawczyk, Rose McCarty, Bartosz Walczak

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Author Details

James Davies
  • Department of Combinatorics and Optimization, School of Mathematics, University of Waterloo, Canada
Tomasz Krawczyk
  • Department of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Rose McCarty
  • Department of Combinatorics and Optimization, School of Mathematics, University of Waterloo, Canada
Bartosz Walczak
  • Department of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

Funding

Tomasz Krawczyk and Bartosz Walczak were partially supported by the National Science Centre of Poland grant 2015/17/D/ST1/00585.

Acknowledgements

We thank Bodhayan Roy for sharing the problem of whether polygon visibility graphs are χ-bounded.

Cite As Get BibTex

James Davies, Tomasz Krawczyk, Rose McCarty, and Bartosz Walczak. Colouring Polygon Visibility Graphs and Their Generalizations. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.SoCG.2021.29

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Visibility graphs
  • χ-boundedness
  • pseudoline arrangements
  • ordered graphs

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