Visibility Graphs of Point Sets in the Plane

The visibility graph 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 V(X Z2 ) 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 K

• Type: Journal
• Year: 2008
• Where: DCG
• Authors: Florian Pfender
• Keywords: DCG 2008, Discrete Point, Edge Xy, Visibility Graphs