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}
}
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Keywords: |
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Disk packing, planar graphs, contact representation |
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Collection: |
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2nd Symposium on Simplicity in Algorithms (SOSA 2019) |
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Issue Date: |
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2018 |
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Date of publication: |
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08.01.2019 |
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)