On rooted directed path graphs

Autores
Tondato, Silvia Beatriz; Gutiérrez, Marisa
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. An asteroidal quadruple is a stable set of four vertices such that any three of them is an asteroidal triple. Two non adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex-disjoint chordless paths satisfying certain technical conditions. Cameron, Ho`ang, and L´evˆeque [DIMAP Workshop on Algorithmic Graph Theory, 67–74, Electron. Notes Discrete Math., 32, Elsevier, 2009] proved that if a pair of non adjacent vertices are linked by a special connection then in any directed path model T the subpaths of T corresponding to the vertices forming the special connection have to overlap and they force T to be completely directed in one direction between these vertices. Special connections along with the concept of asteroidal quadruple play an important role to study rooted directed path graphs, which are the intersection graphs of directed paths in a rooted directed tree. In this work we define other special connections; these special connections along with the ones defined by Cameron, Ho`ang, and L´evˆeque are nine in total, and we prove that every one forces T to be completely directed in one direction between these vertices. Also, we give a characterization of rooted directed path graphs whose rooted models cannot be rooted on a bold maximal clique. As a by-product of our result, we build new forbidden induced subgraphs for rooted directed path graphs.
Facultad de Ciencias Exactas
Consejo Nacional de Investigaciones Científicas y Técnicas
Materia
Matemática
Path
Asteroidals
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/95936

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spelling On rooted directed path graphsTondato, Silvia BeatrizGutiérrez, MarisaMatemáticaPathAsteroidalsAn asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. An asteroidal quadruple is a stable set of four vertices such that any three of them is an asteroidal triple. Two non adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex-disjoint chordless paths satisfying certain technical conditions. Cameron, Ho`ang, and L´evˆeque [DIMAP Workshop on Algorithmic Graph Theory, 67–74, Electron. Notes Discrete Math., 32, Elsevier, 2009] proved that if a pair of non adjacent vertices are linked by a special connection then in any directed path model T the subpaths of T corresponding to the vertices forming the special connection have to overlap and they force T to be completely directed in one direction between these vertices. Special connections along with the concept of asteroidal quadruple play an important role to study rooted directed path graphs, which are the intersection graphs of directed paths in a rooted directed tree. In this work we define other special connections; these special connections along with the ones defined by Cameron, Ho`ang, and L´evˆeque are nine in total, and we prove that every one forces T to be completely directed in one direction between these vertices. Also, we give a characterization of rooted directed path graphs whose rooted models cannot be rooted on a bold maximal clique. As a by-product of our result, we build new forbidden induced subgraphs for rooted directed path graphs.Facultad de Ciencias ExactasConsejo Nacional de Investigaciones Científicas y Técnicas2016-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf114-144http://sedici.unlp.edu.ar/handle/10915/95936enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/55216info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v57n1/v57n1a09.pdfinfo:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol57info:eu-repo/semantics/altIdentifier/hdl/11336/55216info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T10:52:27Zoai:sedici.unlp.edu.ar:10915/95936Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 10:52:27.445SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv On rooted directed path graphs
title On rooted directed path graphs
spellingShingle On rooted directed path graphs
Tondato, Silvia Beatriz
Matemática
Path
Asteroidals
title_short On rooted directed path graphs
title_full On rooted directed path graphs
title_fullStr On rooted directed path graphs
title_full_unstemmed On rooted directed path graphs
title_sort On rooted directed path graphs
dc.creator.none.fl_str_mv Tondato, Silvia Beatriz
Gutiérrez, Marisa
author Tondato, Silvia Beatriz
author_facet Tondato, Silvia Beatriz
Gutiérrez, Marisa
author_role author
author2 Gutiérrez, Marisa
author2_role author
dc.subject.none.fl_str_mv Matemática
Path
Asteroidals
topic Matemática
Path
Asteroidals
dc.description.none.fl_txt_mv An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. An asteroidal quadruple is a stable set of four vertices such that any three of them is an asteroidal triple. Two non adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex-disjoint chordless paths satisfying certain technical conditions. Cameron, Ho`ang, and L´evˆeque [DIMAP Workshop on Algorithmic Graph Theory, 67–74, Electron. Notes Discrete Math., 32, Elsevier, 2009] proved that if a pair of non adjacent vertices are linked by a special connection then in any directed path model T the subpaths of T corresponding to the vertices forming the special connection have to overlap and they force T to be completely directed in one direction between these vertices. Special connections along with the concept of asteroidal quadruple play an important role to study rooted directed path graphs, which are the intersection graphs of directed paths in a rooted directed tree. In this work we define other special connections; these special connections along with the ones defined by Cameron, Ho`ang, and L´evˆeque are nine in total, and we prove that every one forces T to be completely directed in one direction between these vertices. Also, we give a characterization of rooted directed path graphs whose rooted models cannot be rooted on a bold maximal clique. As a by-product of our result, we build new forbidden induced subgraphs for rooted directed path graphs.
Facultad de Ciencias Exactas
Consejo Nacional de Investigaciones Científicas y Técnicas
description An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. An asteroidal quadruple is a stable set of four vertices such that any three of them is an asteroidal triple. Two non adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex-disjoint chordless paths satisfying certain technical conditions. Cameron, Ho`ang, and L´evˆeque [DIMAP Workshop on Algorithmic Graph Theory, 67–74, Electron. Notes Discrete Math., 32, Elsevier, 2009] proved that if a pair of non adjacent vertices are linked by a special connection then in any directed path model T the subpaths of T corresponding to the vertices forming the special connection have to overlap and they force T to be completely directed in one direction between these vertices. Special connections along with the concept of asteroidal quadruple play an important role to study rooted directed path graphs, which are the intersection graphs of directed paths in a rooted directed tree. In this work we define other special connections; these special connections along with the ones defined by Cameron, Ho`ang, and L´evˆeque are nine in total, and we prove that every one forces T to be completely directed in one direction between these vertices. Also, we give a characterization of rooted directed path graphs whose rooted models cannot be rooted on a bold maximal clique. As a by-product of our result, we build new forbidden induced subgraphs for rooted directed path graphs.
publishDate 2016
dc.date.none.fl_str_mv 2016-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol57
info:eu-repo/semantics/altIdentifier/hdl/11336/55216
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
114-144
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
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