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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/95936
Ver los metadatos del registro completo
id |
SEDICI_0b80d5ba9b9d88ee0fedba44f0ba890d |
---|---|
oai_identifier_str |
oai:sedici.unlp.edu.ar:10915/95936 |
network_acronym_str |
SEDICI |
repository_id_str |
1329 |
network_name_str |
SEDICI (UNLP) |
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 Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://sedici.unlp.edu.ar/handle/10915/95936 |
url |
http://sedici.unlp.edu.ar/handle/10915/95936 |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/55216 info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v57n1/v57n1a09.pdf 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 http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-sa/4.0/ 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) instname:Universidad Nacional de La Plata instacron:UNLP |
reponame_str |
SEDICI (UNLP) |
collection |
SEDICI (UNLP) |
instname_str |
Universidad Nacional de La Plata |
instacron_str |
UNLP |
institution |
UNLP |
repository.name.fl_str_mv |
SEDICI (UNLP) - Universidad Nacional de La Plata |
repository.mail.fl_str_mv |
alira@sedici.unlp.edu.ar |
_version_ |
1842260406485123072 |
score |
13.13397 |