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

Francisco Santos, Raimund Seidel

Published 2002-04-03, updated 2002-04-18Version 2

We show that a point set of cardinality $n$ in the plane cannot be the vertex set of more than $59^n O(n^{-6})$ straight-edge triangulations of its convex hull. This improves the previous upper bound of $276.75^n$.