Twisted ways to find plane structures in simple drawings of complete graphs

Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). A simple drawing is c-monotone if there is a point O such that each ray emanating from O crosses each edge of the drawing at most once. W...

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Detalles Bibliográficos
Autores: Aichholzer, Oswin, García, Alfredo, Tejel, Javier, Vogtenhuber, Birgit, Weinberger, Alexandra
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Zaragoza
Repositorio:Zaguán. Repositorio Digital de la Universidad de Zaragoza
OAI Identifier:oai:zaguan.unizar.es:132154
Acceso en línea:http://zaguan.unizar.es/record/132154
Access Level:acceso abierto
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spelling Twisted ways to find plane structures in simple drawings of complete graphsAichholzer, OswinGarcía, AlfredoTejel, JavierVogtenhuber, BirgitWeinberger, AlexandraSimple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). A simple drawing is c-monotone if there is a point O such that each ray emanating from O crosses each edge of the drawing at most once. We introduce a special kind of c-monotone drawings that we call generalized twisted drawings. A c-monotone drawing is generalized twisted if there is a ray emanating from O that crosses all the edges of the drawing. Via this class of drawings, we show that every simple drawing of the complete graph with n vertices contains [fórmula] pairwise disjoint edges and a plane cycle (and hence path) of length [fórmula]. Both results improve over best previously published lower bounds. On the way we show several structural results and properties of generalized twisted and c-monotone drawings, some of which we believe to be of independent interest. For example, we show that a drawing D is c-monotone if there exists a point O such that no edge of D is crossed more than once by any ray that emanates from O and passes through a vertex of D.2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://zaguan.unizar.es/record/132154reponame:Zaguán. Repositorio Digital de la Universidad de Zaragozainstname:Universidad de ZaragozaInglésinfo:eu-repo/grantAgreement/ES/DGA/E41-17Rinfo:eu-repo/grantAgreement/EC/H2020/734922This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 734922-CONNECTinfo:eu-repo/grantAgreement/ES/MICIU-AEI/PID2019-104129GB-I00-AEI-10.13039-501100011033info:eu-repo/semantics/openAccessoai:zaguan.unizar.es:1321542026-05-29T13:59:51Z
dc.title.none.fl_str_mv Twisted ways to find plane structures in simple drawings of complete graphs
title Twisted ways to find plane structures in simple drawings of complete graphs
spellingShingle Twisted ways to find plane structures in simple drawings of complete graphs
Aichholzer, Oswin
title_short Twisted ways to find plane structures in simple drawings of complete graphs
title_full Twisted ways to find plane structures in simple drawings of complete graphs
title_fullStr Twisted ways to find plane structures in simple drawings of complete graphs
title_full_unstemmed Twisted ways to find plane structures in simple drawings of complete graphs
title_sort Twisted ways to find plane structures in simple drawings of complete graphs
dc.creator.none.fl_str_mv Aichholzer, Oswin
García, Alfredo
Tejel, Javier
Vogtenhuber, Birgit
Weinberger, Alexandra
author Aichholzer, Oswin
author_facet Aichholzer, Oswin
García, Alfredo
Tejel, Javier
Vogtenhuber, Birgit
Weinberger, Alexandra
author_role author
author2 García, Alfredo
Tejel, Javier
Vogtenhuber, Birgit
Weinberger, Alexandra
author2_role author
author
author
author
description Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). A simple drawing is c-monotone if there is a point O such that each ray emanating from O crosses each edge of the drawing at most once. We introduce a special kind of c-monotone drawings that we call generalized twisted drawings. A c-monotone drawing is generalized twisted if there is a ray emanating from O that crosses all the edges of the drawing. Via this class of drawings, we show that every simple drawing of the complete graph with n vertices contains [fórmula] pairwise disjoint edges and a plane cycle (and hence path) of length [fórmula]. Both results improve over best previously published lower bounds. On the way we show several structural results and properties of generalized twisted and c-monotone drawings, some of which we believe to be of independent interest. For example, we show that a drawing D is c-monotone if there exists a point O such that no edge of D is crossed more than once by any ray that emanates from O and passes through a vertex of D.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://zaguan.unizar.es/record/132154
url http://zaguan.unizar.es/record/132154
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/ES/DGA/E41-17R
info:eu-repo/grantAgreement/EC/H2020/734922
This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 734922-CONNECT
info:eu-repo/grantAgreement/ES/MICIU-AEI/PID2019-104129GB-I00-AEI-10.13039-501100011033
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv
publisher.none.fl_str_mv
dc.source.none.fl_str_mv reponame:Zaguán. Repositorio Digital de la Universidad de Zaragoza
instname:Universidad de Zaragoza
instname_str Universidad de Zaragoza
reponame_str Zaguán. Repositorio Digital de la Universidad de Zaragoza
collection Zaguán. Repositorio Digital de la Universidad de Zaragoza
repository.name.fl_str_mv
repository.mail.fl_str_mv
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