Abstract
We describe a 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 coordinatizable yields a simple polygon whose visibility graph is isomorphic to the given graph.
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Abello, Kumar Visibility Graphs and Oriented Matroids. Discrete Comput Geom 28, 449–465 (2002). https://doi.org/10.1007/s00454-002-2881-6
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DOI: https://doi.org/10.1007/s00454-002-2881-6