Tight degree bounds for pseudo-triangulations of points

We show that every set of n points in general position has a minimum pseudo-triangulation whose maximum vertex degree is five. In addition, we demonstrate that every point set in general position has a minimum pseudotriangulation whose maximum face degree is four (i.e., each interior face of this pseudo-triangulation has at most four vertices). Both degree bounds are tight. Minimum pseudo-triangulations realizing these bounds (individually but not jointly) can be constructed in O(nlogn) time. 2002 Elsevier Science B.V. All rights reserved.

• Type: Conference
• Year: 2001
• Where: CCCG
• Authors: Lutz Kettner, David G. Kirkpatrick, Bettina Speckmann
• Keywords: CCCG 2001, CCCG 2007, General Position, Maximum Vertex Degree, Minimum Pseudo-triangulations