On Visibility Graphs of Point Sets in the Plane
Combinatorics
2007-05-23 v1
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 K\'{a}ra, P\'{o}r and Wood.
Cite
@article{arxiv.math/0510467,
title = {On Visibility Graphs of Point Sets in the Plane},
author = {F. Pfender},
journal= {arXiv preprint arXiv:math/0510467},
year = {2007}
}
Comments
4 pages