Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Analytic combinatorics of non-crossing configurations
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
Lower bounds on the number of crossing-free subgraphs of KN
Computational Geometry: Theory and Applications
On the crossing number of complete graphs
Proceedings of the eighteenth annual symposium on Computational geometry
A better upper bound on the number of triangulations of a planar point set
Journal of Combinatorial Theory Series A
Convexity minimizes pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
A lower bound on the number of triangulations of planar point sets
Computational Geometry: Theory and Applications
The Polytope of Non-Crossing Graphs on a Planar Point Set
Discrete & Computational Geometry
Abstract order type extension and new results on the rectilinear crossing number
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On the number of crossing-free matchings, (cycles, and partitions)
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the number of crossing-free matchings, (cycles, and partitions)
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
On the number of pseudo-triangulations of certain point sets
Journal of Combinatorial Theory Series A
The number of triangulations on planar point sets
GD'06 Proceedings of the 14th international conference on Graph drawing
Optimizing regular edge labelings
GD'10 Proceedings of the 18th international conference on Graph drawing
On the number of higher order Delaunay triangulations
Theoretical Computer Science
On the number of higher order delaunay triangulations
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
On the number of cycles in planar graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs and connected plane graphs as well as the number of cycle-free plane graphs is minimized when S is in convex position. Moreover, these results hold for all these graphs with an arbitrary but fixed number of edges. Consequently, we provide simple proofs that the number of spanning trees, cycle-free graphs (forests), perfect matchings, and spanning paths is also minimized for point sets in convex position.In addition we construct a new extremal configuration, the so-called double zig-zag chain. Most noteworthy this example bears Θ*(√72n) = Θ*(8.4853n) triangulations and Θ*(41.1889n) plane graphs (omitting polynomial factors in both cases), improving the previously known best maximizing examples.