Cliques and extended triangles : A necessary condition for planar clique graphs

Autores
Alcón, Liliana Graciela; Gutiérrez, Marisa
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
By generalizing the idea of extended triangle of a graph, we succeed in obtaining a common framework for the result of Roberts and Spencer about clique graphs and the one of Szwarcfiter about Helly graphs. We characterize Helly and 3-Helly planar graphs using extended triangles. We prove that if a planar graph G is a clique graph, then every extended triangle of G must be a clique graph. Finally, we show the extended triangles of a planar graph which are clique graphs. Any one of the obtained characterizations are tested in O(n2) time.
Facultad de Ciencias Exactas
Materia
Matemática
Clique graphs
Extended triangles
Helly graphs
Planar graphs
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:10915/83260
Acceder
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network_acronym_str SEDICI
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network_name_str SEDICI (UNLP)
spelling Cliques and extended triangles : A necessary condition for planar clique graphsAlcón, Liliana GracielaGutiérrez, MarisaMatemáticaClique graphsExtended trianglesHelly graphsPlanar graphsBy generalizing the idea of extended triangle of a graph, we succeed in obtaining a common framework for the result of Roberts and Spencer about clique graphs and the one of Szwarcfiter about Helly graphs. We characterize Helly and 3-Helly planar graphs using extended triangles. We prove that if a planar graph G is a clique graph, then every extended triangle of G must be a clique graph. Finally, we show the extended triangles of a planar graph which are clique graphs. Any one of the obtained characterizations are tested in O(n2) time.Facultad de Ciencias Exactas2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf3-17http://sedici.unlp.edu.ar/handle/10915/83260enginfo:eu-repo/semantics/altIdentifier/issn/0166-218Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/S0166-218X(03)00369-Xinfo: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:UNLP2025-11-05T12:55:11Zoai:sedici.unlp.edu.ar:10915/83260Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-11-05 12:55:12.225SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Cliques and extended triangles : A necessary condition for planar clique graphs
title Cliques and extended triangles : A necessary condition for planar clique graphs
spellingShingle Cliques and extended triangles : A necessary condition for planar clique graphs
Alcón, Liliana Graciela
Matemática
Clique graphs
Extended triangles
Helly graphs
Planar graphs
title_short Cliques and extended triangles : A necessary condition for planar clique graphs
title_full Cliques and extended triangles : A necessary condition for planar clique graphs
title_fullStr Cliques and extended triangles : A necessary condition for planar clique graphs
title_full_unstemmed Cliques and extended triangles : A necessary condition for planar clique graphs
title_sort Cliques and extended triangles : A necessary condition for planar clique graphs
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Gutiérrez, Marisa
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutiérrez, Marisa
author_role author
author2 Gutiérrez, Marisa
author2_role author
dc.subject.none.fl_str_mv Matemática
Clique graphs
Extended triangles
Helly graphs
Planar graphs
topic Matemática
Clique graphs
Extended triangles
Helly graphs
Planar graphs
dc.description.none.fl_txt_mv By generalizing the idea of extended triangle of a graph, we succeed in obtaining a common framework for the result of Roberts and Spencer about clique graphs and the one of Szwarcfiter about Helly graphs. We characterize Helly and 3-Helly planar graphs using extended triangles. We prove that if a planar graph G is a clique graph, then every extended triangle of G must be a clique graph. Finally, we show the extended triangles of a planar graph which are clique graphs. Any one of the obtained characterizations are tested in O(n2) time.
Facultad de Ciencias Exactas
description By generalizing the idea of extended triangle of a graph, we succeed in obtaining a common framework for the result of Roberts and Spencer about clique graphs and the one of Szwarcfiter about Helly graphs. We characterize Helly and 3-Helly planar graphs using extended triangles. We prove that if a planar graph G is a clique graph, then every extended triangle of G must be a clique graph. Finally, we show the extended triangles of a planar graph which are clique graphs. Any one of the obtained characterizations are tested in O(n2) time.
publishDate 2004
dc.date.none.fl_str_mv 2004
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/10915/83260
url http://sedici.unlp.edu.ar/handle/10915/83260
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/S0166-218X(03)00369-X
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)
dc.format.none.fl_str_mv application/pdf
3-17
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
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reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
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repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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