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3-colorability of pseudo-triangulations

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10.1142/S0218195915500168
 
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hdl:2117/85279

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Aichholzer, Oswin
Aurenhammer, Franz
Hackl, Thomas
Huemer, ClemensMés informacióMés informacióMés informació
Pilz, Alexander
Vogtenhuber, Birgit
Document typeArticle
Defense date2015
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
This work is protected by the corresponding intellectual and industrial property rights. Except where otherwise noted, its contents are licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
Deciding 3-colorability for general plane graphs is known to be an NP-complete problem. However, for certain families of graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudo-triangulations, which are a generalization of triangulations, and prove NP-completeness for this class. This result also holds if we bound their face degree to four, or exclusively consider pointed pseudo-triangulations with maximum face degree five. In contrast to these completeness results, we show that pointed pseudo-triangulations with maximum face degree four are always 3-colorable. An according 3-coloring can be found in linear time. Some complexity results relating to the rank of pseudo-triangulations are also given.
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Electronic version of an article published as International Journal of Computational Geometry & Applications, Vol. 25, No. 4 (2015) 283–298 DOI: 10.1142/S0218195915500168 © 2015 World Scientific Publishing Company. http://www.worldscientific.com/worldscinet/ijcga
CitationAichholzer, O., Aurenhammer, F., Hackl, T., Huemer, C., Pilz, A., Vogtenhuber, B. 3-colorability of pseudo-triangulations. "International journal of computational geometry and applications", 2015, vol. 25, núm. 4, p. 283-298. 
URIhttp://hdl.handle.net/2117/85279
DOI10.1142/S0218195915500168
ISSN0218-1959
Publisher versionhttp://www.worldscientific.com/worldscinet/ijcga
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  • DCCG - Grup de recerca en geometria computacional, combinatoria i discreta - Articles de revista [85]
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