We exhibit a family of graphs which can be realized as pseudo-visibility graphs of pseudo-polygons, but not of straight-line polygons. The construction is based on the characterization of vertex-edge pseudo-visibility graphs of O'Rourke and Streinu ORS96 and extends recent results on non-stretchable vertex-edge visibility graphs of Streinu Str99 . We show that there is a pseudo-visibility graphs for which there exists only one of vertex-edge visibility graph compatible with it, which is then shown to be non-stretchable. The construction is then extended to an in nite family.
Streinu REF constructs a pseudo-visibility graph for which there exists a unique compatible vertex-edge visibility graph, which is then shown to be non-stretchable.
Non-stretchable pseudo-visibility graphs
CCCG
Computer Science Mathematics