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CORR
2010
Springer

Counting Plane Graphs: Flippability and its Applications

8 years 11 months ago
Counting Plane Graphs: Flippability and its Applications
We generalize the notions of flippable and simultaneously-flippable edges in a triangulation of a set S of points in the plane, into so called pseudo simultaneously-flippable edges. Such edges are related to the notion of convex decompositions spanned by S. We derive a worst-case tight lower bound on the number of pseudo simultaneouslyflippable edges in any triangulation, and use this bound to obtain upper bounds for the maximal number of several types of plane graphs that can be embedded (with crossing-free straight edges) on a fixed set of N points in the plane. More specifically, denoting by tr(N) < 30N the maximum possible number of triangulations of a set of N points in the plane, we show that every set of N points in the plane can have at most 6.9283N
Michael Hoffmann, Micha Sharir, Adam Sheffer, Csab
Added 01 Mar 2011
Updated 01 Mar 2011
Type Journal
Year 2010
Where CORR
Authors Michael Hoffmann, Micha Sharir, Adam Sheffer, Csaba D. Tóth, Emo Welzl
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