 
Summary: Towards Compatible Triangulations
Oswin Aichholzer
Franz Aurenhammer
Hannes Krasser y
Institute for Theoretical Computer Science
Graz University of Technology, Graz, Austria
foaich,auren,hkrasserg@igi.tugraz.ac.at
Ferran Hurtado z
Departament de Matematica Aplicada II
Universitat Politecnica de Catalunya, Barcelona, Spain
hurtado@ma2.upc.es
Abstract
We state the following conjecture: any two planar npoint 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 satises 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
