Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Polygonizations of point sets in the plane
Discrete & Computational Geometry
Journal of Algorithms
Lower bounds on the number of crossing-free subgraphs of KN
Computational Geometry: Theory and Applications
A better upper bound on the number of triangulations of a planar point set
Journal of Combinatorial Theory Series A
Studies in computational geometry motivated by mesh generation
Studies in computational geometry motivated by mesh generation
On the Number of Simple Cycles in Planar Graphs
Combinatorics, Probability and Computing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Minimum weight triangulation by cutting out triangles
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Random triangulations of planar point sets
Proceedings of the twenty-second annual symposium on Computational geometry
Finding and enumerating Hamilton cycles in 4-regular graphs
Theoretical Computer Science
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Minimum weight triangulation by cutting out triangles
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
The point-set embeddability problem for plane graphs
Proceedings of the twenty-eighth annual symposium on Computational geometry
On the number of cycles in planar graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Bichromatic compatible matchings
Proceedings of the twenty-ninth annual symposium on Computational geometry
| Hi-index | 0.00 |
We show that a set of n points in the plane has at most O(10.05n) perfect matchings with crossing-free straight-line embedding. The expected number of perfect crossing-free matchings of a set of n points drawn i.i.d. from an arbitrary distribution in the plane is at most O(9.24n).Several related bounds are derived: (a) The number of all (not necessarily perfect) crossing-free matchings is at most O(10.43n). (b) The number of left-right perfect crossing-free matchings (where the points are designated as left or as right endpoints of the matching edges) is at most O(5.38n). (c) The number of perfect crossing-free matchings across a line (where all the matching edges must cross a fixed halving line of the set) is at most 4n.These bounds are employed to infer that a set of n points in the plane has at most O(86.81n) crossing-free spanning cycles (simple polygonizations), and at most O(12.24n) crossing-free partitions (partitions of the point set, so that the convex hulls of the individual parts are pairwise disjoint).