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Towards Compatible Triangulations Oswin Aichholzer

Summary: Towards Compatible Triangulations
Oswin Aichholzer 
Franz Aurenhammer
Hannes Krasser y
Institute for Theoretical Computer Science
Graz University of Technology, Graz, Austria
Ferran Hurtado z
Departament de Matematica Aplicada II
Universitat Politecnica de Catalunya, Barcelona, Spain
We state the following conjecture: any two planar n-point sets (that agree
on the number of convex hull points) can be triangulated in a compatible
manner, i.e., such that the resulting two planar graphs are isomorphic.
The conjecture is proved true for point sets with at most three interior
points. We further exhibit a class of point sets which can be triangulated
compatibly with any other set (that satis es the obvious size and hull re-
strictions). Finally, we prove that adding a small number of Steiner points
(the number of interior points minus two) always allows for compatible


Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universitšt Graz
Krasser, Hannes - Institute for Theoretical Computer Science, Technische Universitšt Graz
Technische Universitšt Graz, Institute for Software Technology


Collections: Computer Technologies and Information Sciences