Graphs with large total angular resolution

The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the...

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Detalhes bibliográficos
Autores: Aichholzer, Oswin, Korman Cozzetti, Matías, Okamoto, Yoshio, Parada Muñoz, Irene María de|||0000-0003-3147-0083, Perz, Daniel, van Renssen, Andre, Vogtenhuber, Birgit
Formato: artículo
Fecha de publicación:2023
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/404001
Acesso em linha:https://hdl.handle.net/2117/404001
https://dx.doi.org/10.1016/j.tcs.2022.12.010
Access Level:acceso abierto
Palavra-chave:Computer science--Mathematics
Graph theory
Graph drawing
Total angular resolution
Angular resolution
Crossing resolution
NP-hardness.
Informàtica--Matemàtica
Grafs, Teoria de
Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
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oai_identifier_str oai:upcommons.upc.edu:2117/404001
network_acronym_str ES
network_name_str España
repository_id_str
spelling Graphs with large total angular resolutionAichholzer, OswinKorman Cozzetti, MatíasOkamoto, YoshioParada Muñoz, Irene María de|||0000-0003-3147-0083Perz, Danielvan Renssen, AndreVogtenhuber, BirgitComputer science--MathematicsGraph theoryGraph drawingTotal angular resolutionAngular resolutionCrossing resolutionNP-hardness.Informàtica--MatemàticaGrafs, Teoria deClassificació AMS::68 Computer science::68R Discrete mathematics in relation to computer scienceClassificació AMS::05 Combinatorics::05C Graph theoryÀrees temàtiques de la UPC::Matemàtiques i estadísticaÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafsThe total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the minimum angle between crossing edges. We consider the total angular resolution of a graph, which is the maximum total angular resolution of a straight-line drawing of this graph. We prove tight bounds for the number of edges for graphs for some values of the total angular resolution up to a finite number of well specified exceptions of constant size. In addition, we show that deciding whether a graph has total angular resolution at least is NP-hard. Further we present some special graphs and their total angular resolution.Peer Reviewed20232023-01-1720242024-03-08journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/404001https://dx.doi.org/10.1016/j.tcs.2022.12.010reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4040012026-05-27T15:37:01Z
dc.title.none.fl_str_mv Graphs with large total angular resolution
title Graphs with large total angular resolution
spellingShingle Graphs with large total angular resolution
Aichholzer, Oswin
Computer science--Mathematics
Graph theory
Graph drawing
Total angular resolution
Angular resolution
Crossing resolution
NP-hardness.
Informàtica--Matemàtica
Grafs, Teoria de
Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
title_short Graphs with large total angular resolution
title_full Graphs with large total angular resolution
title_fullStr Graphs with large total angular resolution
title_full_unstemmed Graphs with large total angular resolution
title_sort Graphs with large total angular resolution
dc.creator.none.fl_str_mv Aichholzer, Oswin
Korman Cozzetti, Matías
Okamoto, Yoshio
Parada Muñoz, Irene María de|||0000-0003-3147-0083
Perz, Daniel
van Renssen, Andre
Vogtenhuber, Birgit
author Aichholzer, Oswin
author_facet Aichholzer, Oswin
Korman Cozzetti, Matías
Okamoto, Yoshio
Parada Muñoz, Irene María de|||0000-0003-3147-0083
Perz, Daniel
van Renssen, Andre
Vogtenhuber, Birgit
author_role author
author2 Korman Cozzetti, Matías
Okamoto, Yoshio
Parada Muñoz, Irene María de|||0000-0003-3147-0083
Perz, Daniel
van Renssen, Andre
Vogtenhuber, Birgit
author2_role author
author
author
author
author
author
dc.subject.none.fl_str_mv Computer science--Mathematics
Graph theory
Graph drawing
Total angular resolution
Angular resolution
Crossing resolution
NP-hardness.
Informàtica--Matemàtica
Grafs, Teoria de
Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
topic Computer science--Mathematics
Graph theory
Graph drawing
Total angular resolution
Angular resolution
Crossing resolution
NP-hardness.
Informàtica--Matemàtica
Grafs, Teoria de
Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
description The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the minimum angle between crossing edges. We consider the total angular resolution of a graph, which is the maximum total angular resolution of a straight-line drawing of this graph. We prove tight bounds for the number of edges for graphs for some values of the total angular resolution up to a finite number of well specified exceptions of constant size. In addition, we show that deciding whether a graph has total angular resolution at least is NP-hard. Further we present some special graphs and their total angular resolution.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-01-17
2024
2024-03-08
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/2117/404001
https://dx.doi.org/10.1016/j.tcs.2022.12.010
url https://hdl.handle.net/2117/404001
https://dx.doi.org/10.1016/j.tcs.2022.12.010
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-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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
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score 15.300719

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