On Models of Directed Path Graphs Non Rooted Directed Path Graphs

Autores
Gutierrez, Marisa; Tondato, Silvia Beatriz
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted directed path graph is the intersection graph of a family of directed subpaths of a rooted tree. Clearly, rooted directed path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted directed path graphs. With the purpose of proving knowledge in this direction, we show in this paper properties of directed path models that can not be rooted for chordal graphs with any leafage and with leafage four. Therefore, we prove that for leafage four directed path graphs minimally non rooted directed path graphs have a unique asteroidal quadruple, and can be characterized by the presence of certain type of asteroidal quadruples.
Fil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Tondato, Silvia Beatriz. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Materia
ASTEROIDAL QUADRUPLES
CLIQUE TREES
ROOTED DIRECTED PATH GRAPHS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/54360
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/54360
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On Models of Directed Path Graphs Non Rooted Directed Path GraphsGutierrez, MarisaTondato, Silvia BeatrizASTEROIDAL QUADRUPLESCLIQUE TREESROOTED DIRECTED PATH GRAPHShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted directed path graph is the intersection graph of a family of directed subpaths of a rooted tree. Clearly, rooted directed path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted directed path graphs. With the purpose of proving knowledge in this direction, we show in this paper properties of directed path models that can not be rooted for chordal graphs with any leafage and with leafage four. Therefore, we prove that for leafage four directed path graphs minimally non rooted directed path graphs have a unique asteroidal quadruple, and can be characterized by the presence of certain type of asteroidal quadruples.Fil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Tondato, Silvia Beatriz. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaSpringer Tokyo2016-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/54360Gutierrez, Marisa; Tondato, Silvia Beatriz; On Models of Directed Path Graphs Non Rooted Directed Path Graphs; Springer Tokyo; Graphs And Combinatorics; 32; 2; 3-2016; 663-6840911-0119CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00373-015-1600-zinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00373-015-1600-zinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:09:27Zoai:ri.conicet.gov.ar:11336/54360instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:09:27.337CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On Models of Directed Path Graphs Non Rooted Directed Path Graphs
title On Models of Directed Path Graphs Non Rooted Directed Path Graphs
spellingShingle On Models of Directed Path Graphs Non Rooted Directed Path Graphs
Gutierrez, Marisa
ASTEROIDAL QUADRUPLES
CLIQUE TREES
ROOTED DIRECTED PATH GRAPHS
title_short On Models of Directed Path Graphs Non Rooted Directed Path Graphs
title_full On Models of Directed Path Graphs Non Rooted Directed Path Graphs
title_fullStr On Models of Directed Path Graphs Non Rooted Directed Path Graphs
title_full_unstemmed On Models of Directed Path Graphs Non Rooted Directed Path Graphs
title_sort On Models of Directed Path Graphs Non Rooted Directed Path Graphs
dc.creator.none.fl_str_mv Gutierrez, Marisa
Tondato, Silvia Beatriz
author Gutierrez, Marisa
author_facet Gutierrez, Marisa
Tondato, Silvia Beatriz
author_role author
author2 Tondato, Silvia Beatriz
author2_role author
dc.subject.none.fl_str_mv ASTEROIDAL QUADRUPLES
CLIQUE TREES
ROOTED DIRECTED PATH GRAPHS
topic ASTEROIDAL QUADRUPLES
CLIQUE TREES
ROOTED DIRECTED PATH GRAPHS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted directed path graph is the intersection graph of a family of directed subpaths of a rooted tree. Clearly, rooted directed path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted directed path graphs. With the purpose of proving knowledge in this direction, we show in this paper properties of directed path models that can not be rooted for chordal graphs with any leafage and with leafage four. Therefore, we prove that for leafage four directed path graphs minimally non rooted directed path graphs have a unique asteroidal quadruple, and can be characterized by the presence of certain type of asteroidal quadruples.
Fil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Tondato, Silvia Beatriz. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
description A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted directed path graph is the intersection graph of a family of directed subpaths of a rooted tree. Clearly, rooted directed path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted directed path graphs. With the purpose of proving knowledge in this direction, we show in this paper properties of directed path models that can not be rooted for chordal graphs with any leafage and with leafage four. Therefore, we prove that for leafage four directed path graphs minimally non rooted directed path graphs have a unique asteroidal quadruple, and can be characterized by the presence of certain type of asteroidal quadruples.
publishDate 2016
dc.date.none.fl_str_mv 2016-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/54360
Gutierrez, Marisa; Tondato, Silvia Beatriz; On Models of Directed Path Graphs Non Rooted Directed Path Graphs; Springer Tokyo; Graphs And Combinatorics; 32; 2; 3-2016; 663-684
0911-0119
CONICET Digital
CONICET
url http://hdl.handle.net/11336/54360
identifier_str_mv Gutierrez, Marisa; Tondato, Silvia Beatriz; On Models of Directed Path Graphs Non Rooted Directed Path Graphs; Springer Tokyo; Graphs And Combinatorics; 32; 2; 3-2016; 663-684
0911-0119
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00373-015-1600-z
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00373-015-1600-z
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Tokyo
publisher.none.fl_str_mv Springer Tokyo
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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