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Discrete & Computational Geometry

, Volume 39, Issue 1–3, pp 455–459 | Cite as

Visibility Graphs of Point Sets in the Plane

  • Florian PfenderEmail author
Article

Abstract

The visibility graph \(\mathcal {V}(X)\) of a discrete point set X⊂ℝ2 has vertex set X and an edge xy for every two points x,yX whenever there is no other point in X on the line segment between x and y. We show that for every graph G, there is a point set X∈ℝ2, such that the subgraph of \(\mathcal {V}(X\cup \mathbb {Z}^{2})\) induced by X is isomorphic to G. As a consequence, we show that there are visibility graphs of arbitrary high chromatic number with clique number 6 settling a question by Kára, Pór and Wood.

Keywords

Line Segment Prime Number Chromatic Number Discrete Comput Geom 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.

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.MA 6-2TU BerlinBerlinGermany

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