Determining what sets of trees can be the clique trees of a chordal graph

Autores
de Caria, Pablo Jesús; Gutierrez, Marisa
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Chordal graphs have characteristic tree representations, the clique trees. The problems of finding one or enumerating them have already been solved in a satisfactory way. In this paper, the following related problem is studied: given a family T of trees, all having the same vertex set V, determine whether there exists a chordal graph whose set of clique trees equals T. For that purpose, we undertake a study of the structural properties, some already known and some new, of the clique trees of a chordal graph and the characteristics of the sets that induce subtrees of every clique tree. Some necessary and sufficient conditions and examples of how they can be applied are found, eventually establishing that a positive or negative answer to the problem can be obtained in polynomial time. If affirmative, a graph whose set of clique trees equals T is also obtained. Finally, all the chordal graphs with set of clique trees equal to T are characterized.
Fil: de Caria, Pablo Jesús. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Materia
Chordal Graph
Clique
Clique Tree
Minimal Separator
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/81353
Acceder
id CONICETDig_38979a270be4341cc50e0bcc220fe0b2
oai_identifier_str oai:ri.conicet.gov.ar:11336/81353
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Determining what sets of trees can be the clique trees of a chordal graphde Caria, Pablo JesúsGutierrez, MarisaChordal GraphCliqueClique TreeMinimal Separatorhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Chordal graphs have characteristic tree representations, the clique trees. The problems of finding one or enumerating them have already been solved in a satisfactory way. In this paper, the following related problem is studied: given a family T of trees, all having the same vertex set V, determine whether there exists a chordal graph whose set of clique trees equals T. For that purpose, we undertake a study of the structural properties, some already known and some new, of the clique trees of a chordal graph and the characteristics of the sets that induce subtrees of every clique tree. Some necessary and sufficient conditions and examples of how they can be applied are found, eventually establishing that a positive or negative answer to the problem can be obtained in polynomial time. If affirmative, a graph whose set of clique trees equals T is also obtained. Finally, all the chordal graphs with set of clique trees equal to T are characterized.Fil: de Caria, Pablo Jesús. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaSpringer2012-06-22info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/81353de Caria, Pablo Jesús; Gutierrez, Marisa; Determining what sets of trees can be the clique trees of a chordal graph; Springer; Journal Of The Brazilian Computer Society; 18; 2; 22-6-2012; 121-1280104-65001678-4804CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs13173-011-0048-0info:eu-repo/semantics/altIdentifier/doi/10.1007/s13173-011-0048-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:43:25Zoai:ri.conicet.gov.ar:11336/81353instacron: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 09:43:25.829CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Determining what sets of trees can be the clique trees of a chordal graph
title Determining what sets of trees can be the clique trees of a chordal graph
spellingShingle Determining what sets of trees can be the clique trees of a chordal graph
de Caria, Pablo Jesús
Chordal Graph
Clique
Clique Tree
Minimal Separator
title_short Determining what sets of trees can be the clique trees of a chordal graph
title_full Determining what sets of trees can be the clique trees of a chordal graph
title_fullStr Determining what sets of trees can be the clique trees of a chordal graph
title_full_unstemmed Determining what sets of trees can be the clique trees of a chordal graph
title_sort Determining what sets of trees can be the clique trees of a chordal graph
dc.creator.none.fl_str_mv de Caria, Pablo Jesús
Gutierrez, Marisa
author de Caria, Pablo Jesús
author_facet de Caria, Pablo Jesús
Gutierrez, Marisa
author_role author
author2 Gutierrez, Marisa
author2_role author
dc.subject.none.fl_str_mv Chordal Graph
Clique
Clique Tree
Minimal Separator
topic Chordal Graph
Clique
Clique Tree
Minimal Separator
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Chordal graphs have characteristic tree representations, the clique trees. The problems of finding one or enumerating them have already been solved in a satisfactory way. In this paper, the following related problem is studied: given a family T of trees, all having the same vertex set V, determine whether there exists a chordal graph whose set of clique trees equals T. For that purpose, we undertake a study of the structural properties, some already known and some new, of the clique trees of a chordal graph and the characteristics of the sets that induce subtrees of every clique tree. Some necessary and sufficient conditions and examples of how they can be applied are found, eventually establishing that a positive or negative answer to the problem can be obtained in polynomial time. If affirmative, a graph whose set of clique trees equals T is also obtained. Finally, all the chordal graphs with set of clique trees equal to T are characterized.
Fil: de Caria, Pablo Jesús. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
description Chordal graphs have characteristic tree representations, the clique trees. The problems of finding one or enumerating them have already been solved in a satisfactory way. In this paper, the following related problem is studied: given a family T of trees, all having the same vertex set V, determine whether there exists a chordal graph whose set of clique trees equals T. For that purpose, we undertake a study of the structural properties, some already known and some new, of the clique trees of a chordal graph and the characteristics of the sets that induce subtrees of every clique tree. Some necessary and sufficient conditions and examples of how they can be applied are found, eventually establishing that a positive or negative answer to the problem can be obtained in polynomial time. If affirmative, a graph whose set of clique trees equals T is also obtained. Finally, all the chordal graphs with set of clique trees equal to T are characterized.
publishDate 2012
dc.date.none.fl_str_mv 2012-06-22
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/11336/81353
de Caria, Pablo Jesús; Gutierrez, Marisa; Determining what sets of trees can be the clique trees of a chordal graph; Springer; Journal Of The Brazilian Computer Society; 18; 2; 22-6-2012; 121-128
0104-6500
1678-4804
CONICET Digital
CONICET
url http://hdl.handle.net/11336/81353
identifier_str_mv de Caria, Pablo Jesús; Gutierrez, Marisa; Determining what sets of trees can be the clique trees of a chordal graph; Springer; Journal Of The Brazilian Computer Society; 18; 2; 22-6-2012; 121-128
0104-6500
1678-4804
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs13173-011-0048-0
info:eu-repo/semantics/altIdentifier/doi/10.1007/s13173-011-0048-0
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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
_version_ 1842268601388630016
score 13.13397

Publicaciones similares