# Visibility Graphs of Point Sets in the Plane

Discrete & Computational Geometry, Mar 2008

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,y∈X 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.

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Florian Pfender. Visibility Graphs of Point Sets in the Plane, Discrete & Computational Geometry, 2008, 455-459, DOI: 10.1007/s00454-008-9056-z