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

Autores
De Caria, Pablo Jesús; Gutiérrez, 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) and Gutierrez (1996). 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.
Facultad de Ciencias Exactas
Materia
Matemática
Chordal
Clique
Dually chordal
Neighborhood
Separator
Tree
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/83624

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spelling On minimal vertex separators of dually chordal graphs: properties and characterizationsDe Caria, Pablo JesúsGutiérrez, MarisaMatemáticaChordalCliqueDually chordalNeighborhoodSeparatorTreeMany works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) and Gutierrez (1996). 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.Facultad de Ciencias Exactas2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf2627-2635http://sedici.unlp.edu.ar/handle/10915/83624enginfo:eu-repo/semantics/altIdentifier/issn/0166-218Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2012.02.022info: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:UNLP2025-09-29T11:15:55Zoai:sedici.unlp.edu.ar:10915/83624Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:15:55.809SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Matemática
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
Gutiérrez, Marisa
author De Caria, Pablo Jesús
author_facet De Caria, Pablo Jesús
Gutiérrez, Marisa
author_role author
author2 Gutiérrez, Marisa
author2_role author
dc.subject.none.fl_str_mv Matemática
Chordal
Clique
Dually chordal
Neighborhood
Separator
Tree
topic Matemática
Chordal
Clique
Dually chordal
Neighborhood
Separator
Tree
dc.description.none.fl_txt_mv Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) and Gutierrez (1996). 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.
Facultad de Ciencias Exactas
description Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) and Gutierrez (1996). 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
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info:eu-repo/semantics/publishedVersion
Articulo
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dc.language.none.fl_str_mv eng
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dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0166-218X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2012.02.022
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)
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2627-2635
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