On minimal vertex separators of dually chordal graphs: properties and characterizations
- Autores
- de Caria, Pablo Jesús; Gutierrez, Marisa
- Año de publicación
- 2012
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
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; Argentina
Fil: 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; Argentina - Materia
-
CHORDAL
CLIQUE
DUALLY CHORDAL
NEIGHBORHOOD
SEPARATOR
TREE - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/190841
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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 Técnicas2025-09-29T09:43:23Zoai: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:34982025-09-29 09:43:24.053CONICET 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 |
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 |
topic |
CHORDAL CLIQUE DUALLY CHORDAL NEIGHBORHOOD SEPARATOR TREE |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
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. 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; Argentina Fil: 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; Argentina |
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 |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.070432 |