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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/83624
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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 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo 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://sedici.unlp.edu.ar/handle/10915/83624 |
url |
http://sedici.unlp.edu.ar/handle/10915/83624 |
dc.language.none.fl_str_mv |
eng |
language |
eng |
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) |
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openAccess |
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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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application/pdf 2627-2635 |
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