On minimal vertex separators of dually chordal graphs: properties and characterizations

Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) [1] and Gutierrez (1996) [6]. We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition...

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Detalles Bibliográficos
Autores: de Caria, Pablo Jesús, Gutierrez, Marisa
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/190841
Acceso en línea:http://hdl.handle.net/11336/190841
Access Level:acceso abierto
Palabra clave:CHORDAL
CLIQUE
DUALLY CHORDAL
NEIGHBORHOOD
SEPARATOR
TREE
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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oai_identifier_str oai:ri.conicet.gov.ar:11336/190841
network_acronym_str AR
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repository_id_str
spelling On minimal vertex separators of dually chordal graphs: properties and characterizationsde Caria, Pablo JesúsGutierrez, MarisaCHORDALCLIQUEDUALLY CHORDALNEIGHBORHOODSEPARATORTREEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) [1] and Gutierrez (1996) [6]. We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition for every minimal vertex separator to be contained in the closed neighborhood of a vertex and two major characterizations of dually chordal graphs are proved. The first states that a graph is dually chordal if and only if it possesses a spanning tree such that every minimal vertex separator induces a subtree. The second says that a graph is dually chordal if and only if the family of minimal vertex separators is Helly, its intersection graph is chordal and each of its members induces a connected subgraph. We also found adaptations for them, requiring just O(|E(G)|) minimal vertex separators if they are conveniently chosen. We obtain at the end a proof of a known characterization of the class of hereditary dually chordal graphs that relies on the properties of minimal vertex separators.Fil: de Caria, Pablo Jesús. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaElsevier Science2012-03info: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/11336/190841de Caria, Pablo Jesús; Gutierrez, Marisa; On minimal vertex separators of dually chordal graphs: properties and characterizations; Elsevier Science; Discrete Applied Mathematics; 160; 18; 3-2012; 2627-26350166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0166218X12000832info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2012.02.022info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:41:00Zoai:ri.conicet.gov.ar:11336/190841instacron: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:34982024-05-08 13:41:00.562CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On minimal vertex separators of dually chordal graphs: properties and characterizations
title On minimal vertex separators of dually chordal graphs: properties and characterizations
spellingShingle On minimal vertex separators of dually chordal graphs: properties and characterizations
de Caria, Pablo Jesús
CHORDAL
CLIQUE
DUALLY CHORDAL
NEIGHBORHOOD
SEPARATOR
TREE
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short On minimal vertex separators of dually chordal graphs: properties and characterizations
title_full On minimal vertex separators of dually chordal graphs: properties and characterizations
title_fullStr On minimal vertex separators of dually chordal graphs: properties and characterizations
title_full_unstemmed On minimal vertex separators of dually chordal graphs: properties and characterizations
title_sort On minimal vertex separators of dually chordal graphs: properties and characterizations
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
CLIQUE
DUALLY CHORDAL
NEIGHBORHOOD
SEPARATOR
TREE
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic CHORDAL
CLIQUE
DUALLY CHORDAL
NEIGHBORHOOD
SEPARATOR
TREE
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) [1] and Gutierrez (1996) [6]. We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition for every minimal vertex separator to be contained in the closed neighborhood of a vertex and two major characterizations of dually chordal graphs are proved. The first states that a graph is dually chordal if and only if it possesses a spanning tree such that every minimal vertex separator induces a subtree. The second says that a graph is dually chordal if and only if the family of minimal vertex separators is Helly, its intersection graph is chordal and each of its members induces a connected subgraph. We also found adaptations for them, requiring just O(|E(G)|) minimal vertex separators if they are conveniently chosen. We obtain at the end a proof of a known characterization of the class of hereditary dually chordal graphs that relies on the properties of minimal vertex separators.
publishDate 2012
dc.date.none.fl_str_mv 2012-03
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/11336/190841
de Caria, Pablo Jesús; Gutierrez, Marisa; On minimal vertex separators of dually chordal graphs: properties and characterizations; Elsevier Science; Discrete Applied Mathematics; 160; 18; 3-2012; 2627-2635
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/190841
identifier_str_mv de Caria, Pablo Jesús; Gutierrez, Marisa; On minimal vertex separators of dually chordal graphs: properties and characterizations; Elsevier Science; Discrete Applied Mathematics; 160; 18; 3-2012; 2627-2635
0166-218X
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://www.sciencedirect.com/science/article/pii/S0166218X12000832
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2012.02.022
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
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,81155

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