Flipping Geometric Triangulations on Hyperbolic Surfaces

Authors Vincent Despré, Jean-Marc Schlenker, Monique Teillaud

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Author Details

Vincent Despré
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Jean-Marc Schlenker
  • Department of Mathematics, University of Luxembourg, Luxembourg
Monique Teillaud
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France

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Vincent Despré, Jean-Marc Schlenker, and Monique Teillaud. Flipping Geometric Triangulations on Hyperbolic Surfaces. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint geodesic segments. We prove that the flip graph of geometric triangulations with fixed vertices of a flat torus or a closed hyperbolic surface is connected. We give upper bounds on the number of edge flips that are necessary to transform any geometric triangulation on such a surface into a Delaunay triangulation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Discrete mathematics
  • Mathematics of computing → Geometric topology
  • Hyperbolic surface
  • Topology
  • Delaunay triangulation
  • Algorithm
  • Flip graph


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