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
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/83260
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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:UNLP2025-09-03T10:48:05Zoai: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:13292025-09-03 10:48:05.947SEDICI (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 |
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2004 |
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eng |
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eng |
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