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Summary: Convexity Minimizes PseudoTriangulations
Oswin Aichholzer #+ Franz Aurenhammer # Hannes Krasser ## Bettina Speckmann §
Abstract
The number of minimum pseudotriangulations is minimized for point sets in convex position.
1 Introduction
A pseudotriangle is a planar polygon with exactly
three convex vertices, called corners. Three reflex
chains of edges join the corners. Let S be a set of
n points in general position in the plane. A pseudo
triangulation for S is a partition of the convex hull
of S into pseudotriangles whose vertex set is S. A
pseudotriangulation is called minimum if it consists of
exactly n - 2 pseudotriangles (and 2n - 3 edges), the
minimum possible. Each vertex of a minimum pseudo
triangulation is pointed, that is, its incident edges span
a convex angle. In fact, minimum pseudotriangulations
can be characterized as maximal planar straightline
graphs where each vertex is pointed [15].
Pseudotriangulations, also called geodesic triangula
tions, have received considerable attention in the last
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