Visibility Graphs and Oriented Matroids (Extended Abstract)
Abello, James and Kumar, Krishna (1995) Visibility Graphs and Oriented Matroids (Extended Abstract). In: Graph Drawing DIMACS International Workshop, GD, October 10–12, 1994, Princeton, New Jersey, USA , pp. 147-158 (Official URL: http://dx.doi.org/10.1007/3-540-58950-3_366).
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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.
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