Lower bounds on the number of crossing-free subgraphs of KN
Computational Geometry: Theory and Applications
Random triangulations of planar point sets
Proceedings of the twenty-second annual symposium on Computational geometry
On the Number of Crossing-Free Matchings, Cycles, and Partitions
SIAM Journal on Computing
On the Number of Plane Geometric Graphs
Graphs and Combinatorics
On the number of pseudo-triangulations of certain point sets
Journal of Combinatorial Theory Series A
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
On constrained minimum pseudotriangulations
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
On the number of spanning trees a planar graph can have
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
On degrees in random triangulations of point sets
Journal of Combinatorial Theory Series A
Counting plane graphs: cross-graph charging schemes
GD'12 Proceedings of the 20th international conference on Graph Drawing
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We study the maximum numbers of pseudo-triangulations and pointed pseudo-triangulations that can be embedded over a specific set of points in the plane or contained in a specific triangulation. We derive the bounds O(5.45^N) and @W(2.41^N) for the maximum number of pointed pseudo-triangulations that can be contained in a specific triangulation over a set of N points. For the number of all pseudo-triangulations contained in a triangulation we derive the bounds O^@?(6.54^N) and @W(3.30^N). We also prove that O^@?(89.1^N) pointed pseudo-triangulations can be embedded over any specific set of N points in the plane, and at most 120^N general pseudo-triangulations.