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.
Work partially supported by NSF grants No: DCR-8603722 and DCR-8896281
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Abello, J., Kumar, K. (1995). Visibility graphs and oriented matroids (extended abstract). In: Tamassia, R., Tollis, I.G. (eds) Graph Drawing. GD 1994. Lecture Notes in Computer Science, vol 894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58950-3_366
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