Visibility Graphs and Oriented Matroids (Extended Abstract)

This paper describes a new set of necessary conditions for a given graph to be the visibility graph of a simple polygon. For every graph satisfying these conditions we show that a uniform rank 3 oriented matroid can be constructed in polynomial time, which if affinely co- ordinatizable would yield a simple polygon whose visibility graph is isomorphic to the given graph. This will in turn offer the first characterization of this class of graphs