Lower bounds on the number of crossing-free subgraphs of K N
TLDR
In this article, the authors improved previous lower bounds on the number of simple polygonizations and other kinds of crossing-free subgraphs of a set of N points in the plane by analyzing a suitable configuration.Abstract:
We improve previous lower bounds on the number of simple polygonizations, and other kinds of crossing-free subgraphs, of a set of N points in the plane by analyzing a suitable configuration. We also prove that the number of crossing-free perfect matchings and spanning trees is minimum when the points are in convex position.read more
Citations
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Journal ArticleDOI
Enumerating Order Types for Small Point Sets with Applications
TL;DR: A complete and reliable data base for all possible order types of size n=10 or less is established and substantiate the usefulness of the data base by applying it to several problems in computational and combinatorial geometry.
Journal ArticleDOI
On the Number of Crossing-Free Matchings, Cycles, and Partitions
Micha Sharir,Emo Welzl +1 more
TL;DR: It is shown that a set ofn points in the plane has at most O(10.05 n) perfect matchings with crossing-free straight-line embedding, and several related bounds are derived.
Journal ArticleDOI
On the Number of Plane Geometric Graphs
Oswin Aichholzer,Thomas Hackl,Clemens Huemer,Ferran Hurtado,Hannes Krasser,Birgit Vogtenhuber +5 more
TL;DR: A unified proof that the cardinality of any family of acyclic graphs (for example spanning trees, forests, perfect matchings, spanning paths, and more) is minimized for point sets in convex position is provided.
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A better upper bound on the number of triangulations of a planar point set
Francisco Santos,Raimund Seidel +1 more
TL;DR: It is shown that a point set of cardinality n in the plane cannot be the vertex set of more than O(59nn-6) straight-edge triangulations of its convex hull.
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Enumeration of noncrossing trees on a circle
TL;DR: Several enumerative problems concerning labelled trees whose vertices lie on a circle and whose edges are rectilinear and do not cross are considered.
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The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
The Art in Computer Programming
Andrew Hunt,Dave Thomas +1 more
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