Non-stretchable pseudo-visibility graphs

Authors:
Ileana Streinu
Affiliations:
Computer Science Department, Smith College, Northampton, MA 01063, USA
Venue:
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Year:
2005

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Abstract

We exhibit a family of graphs which can be realized as pseudo-visibility graphs of pseudo-polygons, but not of straight-line polygons. The example is based on the characterization of vertex-edge pseudo-visibility graphs of O'Rourke and Streinu [Proc. ACM Symp. Comput. Geometry, Nice, France, 1997, pp. 119-128] and extends a recent result of the author [Proc. ACM Symp. Comput. Geometry, Miami Beach, 1999, pp. 274-280] on non-stretchable vertex-edge visibility graphs. We construct a pseudo-visibility graph for which there exists a unique compatible vertex-edge visibility graph, which is then shown to be non-stretchable. The construction is then extended to an infinite family.