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Towards Compatible Triangulations

  • Oswin Aichholzer
  • Franz Aurenhammer
  • Hannes Krasser
  • Ferran Hurtado
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2108)

Abstract

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 restrictions). Finally, we prove that adding a small number of Steiner points (the number of interior points minus two) always allows for compatible triangulations.

Keywords

Extreme Point Interior Point Convex Polygon Order Type Steiner Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Oswin Aichholzer
    • 1
  • Franz Aurenhammer
    • 1
  • Hannes Krasser
    • 1
  • Ferran Hurtado
    • 2
  1. 1.Institute for Theoretical Computer ScienceGraz University of TechnologyGrazAustria
  2. 2.Departament de Matematica Aplicada IIUniversitat Politecnica de CatalunyaBarcelonaSpain

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