Binary labelings for plane quadrangulations and their relatives

Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our labeling resembles many of the properties of Schnyder's one f...

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Authors: Felsner, Stefan, Huemer, Clemens|||0000-0001-7557-0823, Kappes, Sarah, Orden, David
Format: article
Publication Date:2010
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/8923
Online Access:https://hdl.handle.net/2117/8923
Access Level:Open access
Keyword:Combinatorial analysis
Graph theory
Schnyder labeling
Quadrangulation
Book embedding
Pseudo-triangulation
Laman graph
Anàlisi combinatòria
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
id ES_c3a042aa2123d14cfa98e6302e751e82
oai_identifier_str oai:upcommons.upc.edu:2117/8923
network_acronym_str ES
network_name_str España
repository_id_str
spelling Binary labelings for plane quadrangulations and their relativesFelsner, StefanHuemer, Clemens|||0000-0001-7557-0823Kappes, SarahOrden, DavidCombinatorial analysisGraph theorySchnyder labelingQuadrangulationBook embeddingPseudo-triangulationLaman graphAnàlisi combinatòriaGrafs, Teoria deÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::CombinatòriaMotivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our labeling resembles many of the properties of Schnyder's one for triangulations: Apart from being in bijection with tree decompositions, paths in these trees allow to define the regions of a vertex such that counting faces in them yields an algorithm for embedding the quadrangulation, in this case on a 2-book. Furthermore, as Schnyder labelings have been extended to 3-connected plane graphs, we are able to extend our labeling from quadrangulations to a larger class of 2-connected bipartite graphs.20102010-01-0120102010-09-16journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/8923reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/89232026-05-27T15:37:01Z
dc.title.none.fl_str_mv Binary labelings for plane quadrangulations and their relatives
title Binary labelings for plane quadrangulations and their relatives
spellingShingle Binary labelings for plane quadrangulations and their relatives
Felsner, Stefan
Combinatorial analysis
Graph theory
Schnyder labeling
Quadrangulation
Book embedding
Pseudo-triangulation
Laman graph
Anàlisi combinatòria
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
title_short Binary labelings for plane quadrangulations and their relatives
title_full Binary labelings for plane quadrangulations and their relatives
title_fullStr Binary labelings for plane quadrangulations and their relatives
title_full_unstemmed Binary labelings for plane quadrangulations and their relatives
title_sort Binary labelings for plane quadrangulations and their relatives
dc.creator.none.fl_str_mv Felsner, Stefan
Huemer, Clemens|||0000-0001-7557-0823
Kappes, Sarah
Orden, David
author Felsner, Stefan
author_facet Felsner, Stefan
Huemer, Clemens|||0000-0001-7557-0823
Kappes, Sarah
Orden, David
author_role author
author2 Huemer, Clemens|||0000-0001-7557-0823
Kappes, Sarah
Orden, David
author2_role author
author
author
dc.subject.none.fl_str_mv Combinatorial analysis
Graph theory
Schnyder labeling
Quadrangulation
Book embedding
Pseudo-triangulation
Laman graph
Anàlisi combinatòria
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
topic Combinatorial analysis
Graph theory
Schnyder labeling
Quadrangulation
Book embedding
Pseudo-triangulation
Laman graph
Anàlisi combinatòria
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
description Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our labeling resembles many of the properties of Schnyder's one for triangulations: Apart from being in bijection with tree decompositions, paths in these trees allow to define the regions of a vertex such that counting faces in them yields an algorithm for embedding the quadrangulation, in this case on a 2-book. Furthermore, as Schnyder labelings have been extended to 3-connected plane graphs, we are able to extend our labeling from quadrangulations to a larger class of 2-connected bipartite graphs.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-01-01
2010
2010-09-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/8923
url https://hdl.handle.net/2117/8923
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869418811848916992
score 15,300719

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