A better upper bound on the number of triangulations of a planar point set

Authors:
Francisco Santos;Raimund Seidel
Affiliations:
Dept. de Matemáticas, Est. y. Comp, Facultad de Ciencias, Universidad de Cantabria, E-39005 Santander, Spain;FR 6.2 Informatik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
Venue:
Journal of Combinatorial Theory Series A
Year:
2003

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Abstract

We show 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. This improves the previous upper bound of 276.75n+O(log(n)).