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On Visibility Graphs of Point Sets in the Plane

F. Pfender
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Abstract

The visibility graph Vis(X) of a discrete point set X in the plane has vertex set X and an edge xy for every two points x,y\in 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, such that the subgraph of Vis(X\cup 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 six settling a question by Kára, Pór and Wood.

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F. Pfender. 2005-10-21. On Visibility Graphs of Point Sets in the Plane. https://arxiv.org/abs/math/0510467

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