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URN: urn:nbn:de:0030-drops-138305
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Minimal Delaunay Triangulations of Hyperbolic Surfaces

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Abstract

Motivated by recent work on Delaunay triangulations of hyperbolic surfaces, we consider the minimal number of vertices of such triangulations. First, we show that every hyperbolic surface of genus g has a simplicial Delaunay triangulation with O(g) vertices, where edges are given by distance paths. Then, we construct a class of hyperbolic surfaces for which the order of this bound is optimal. Finally, to give a general lower bound, we show that the Ω(√g) lower bound for the number of vertices of a simplicial triangulation of a topological surface of genus g is tight for hyperbolic surfaces as well.

BibTeX - Entry

@InProceedings{ebbens_et_al:LIPIcs.SoCG.2021.31,
  author =	{Ebbens, Matthijs and Parlier, Hugo and Vegter, Gert},
  title =	{{Minimal Delaunay Triangulations of Hyperbolic Surfaces}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13830},
  URN =		{urn:nbn:de:0030-drops-138305},
  doi =		{10.4230/LIPIcs.SoCG.2021.31},
  annote =	{Keywords: Delaunay triangulations, hyperbolic surfaces, metric graph embeddings, moduli spaces}
}

Keywords: Delaunay triangulations, hyperbolic surfaces, metric graph embeddings, moduli spaces
Seminar: 37th International Symposium on Computational Geometry (SoCG 2021)
Issue date: 2021
Date of publication: 02.06.2021


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