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Discrete & Computational Geometry

, Volume 34, Issue 3, pp 497–506 | Cite as

On the Chromatic Number of the Visibility Graph of a Set of Points in the Plane

  • Jan KáraEmail author
  • Attila PórEmail author
  • David R. WoodEmail author
Article

Abstract

The visibility graph V(P) of a point set P \subseteq R2 has vertex set P, such that two points v,w ∈ P are adjacent whenever there is no other point in P on the line segment between v and w. We study the chromatic number of V(P). We characterise the 2- and 3-chromatic visibility graphs. It is an open problem whether the chromatic number of a visibility graph is bounded by its clique number. Our main result is a super-polynomial lower bound on the chromatic number (in terms of the clique number).

Keywords

Computational Mathematic Line Segment Open Problem Chromatic Number Visibility Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Charles University, 118 00 Prague 1 Czech Republic
  2. 2.Departament de Matematica Aplicada II, Universitat Politecnica de Catalunya, E-08034 BarcelonaSpain

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