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DOI: 10.4230/OASIcs.SOSA.2019.8
URN: urn:nbn:de:0030-drops-100349
URL: http://drops.dagstuhl.de/opus/volltexte/2018/10034/
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Felsner, Stefan ; Rote, GŁnter

On Primal-Dual Circle Representations

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OASIcs-SOSA-2019-8.pdf (0.9 MB)


Abstract

The Koebe-Andreev-Thurston Circle Packing Theorem states that every triangulated planar graph has a contact representation by circles. The theorem has been generalized in various ways. The most prominent generalization assures the existence of a primal-dual circle representation for every 3-connected planar graph. We present a simple and elegant elementary proof of this result.

BibTeX - Entry

@InProceedings{felsner_et_al:OASIcs:2018:10034,
  author =	{Stefan Felsner and G{\"u}nter Rote},
  title =	{{On Primal-Dual Circle Representations}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{8:1--8:18},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{69},
  editor =	{Jeremy T. Fineman and Michael Mitzenmacher},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10034},
  URN =		{urn:nbn:de:0030-drops-100349},
  doi =		{10.4230/OASIcs.SOSA.2019.8},
  annote =	{Keywords: Disk packing, planar graphs, contact representation}
}

Keywords: Disk packing, planar graphs, contact representation
Seminar: 2nd Symposium on Simplicity in Algorithms (SOSA 2019)
Issue Date: 2018
Date of publication: 18.12.2018


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