The complexity of clique graph recognition
- Autores
- Alcón, Liliana Graciela; Faria, Luerbio; Figueiredo, Celina M. H. de; Gutiérrez, Marisa
- Año de publicación
- 2009
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- A complete set of a graph G is a subset of vertices inducing a complete subgraph. A clique is a maximal complete set. Denote by C (G) the clique family of G. The clique graph of G, denoted by K (G), is the intersection graph of C (G). Say that G is a clique graph if there exists a graph H such that G = K (H). The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink in 1968, and a characterization was proposed by Roberts and Spencer in 1971. However, the time complexity of the problem of recognizing clique graphs is a long-standing open question. We prove that the clique graph recognition problem is NP-complete.
Facultad de Ciencias Exactas - Materia
-
Matemática
Clique graphs
Helly property
Intersection graphs
NP-complete problems - 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:10915/82662
Ver los metadatos del registro completo
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The complexity of clique graph recognitionAlcón, Liliana GracielaFaria, LuerbioFigueiredo, Celina M. H. deGutiérrez, MarisaMatemáticaClique graphsHelly propertyIntersection graphsNP-complete problemsA complete set of a graph G is a subset of vertices inducing a complete subgraph. A clique is a maximal complete set. Denote by C (G) the clique family of G. The clique graph of G, denoted by K (G), is the intersection graph of C (G). Say that G is a clique graph if there exists a graph H such that G = K (H). The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink in 1968, and a characterization was proposed by Roberts and Spencer in 1971. However, the time complexity of the problem of recognizing clique graphs is a long-standing open question. We prove that the clique graph recognition problem is NP-complete.Facultad de Ciencias Exactas2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf2072-2083http://sedici.unlp.edu.ar/handle/10915/82662enginfo:eu-repo/semantics/altIdentifier/issn/0304-3975info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2009.01.018info: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:UNLP2025-09-03T10:47:51Zoai:sedici.unlp.edu.ar:10915/82662Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 10:47:52.013SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
The complexity of clique graph recognition |
| title |
The complexity of clique graph recognition |
| spellingShingle |
The complexity of clique graph recognition Alcón, Liliana Graciela Matemática Clique graphs Helly property Intersection graphs NP-complete problems |
| title_short |
The complexity of clique graph recognition |
| title_full |
The complexity of clique graph recognition |
| title_fullStr |
The complexity of clique graph recognition |
| title_full_unstemmed |
The complexity of clique graph recognition |
| title_sort |
The complexity of clique graph recognition |
| dc.creator.none.fl_str_mv |
Alcón, Liliana Graciela Faria, Luerbio Figueiredo, Celina M. H. de Gutiérrez, Marisa |
| author |
Alcón, Liliana Graciela |
| author_facet |
Alcón, Liliana Graciela Faria, Luerbio Figueiredo, Celina M. H. de Gutiérrez, Marisa |
| author_role |
author |
| author2 |
Faria, Luerbio Figueiredo, Celina M. H. de Gutiérrez, Marisa |
| author2_role |
author author author |
| dc.subject.none.fl_str_mv |
Matemática Clique graphs Helly property Intersection graphs NP-complete problems |
| topic |
Matemática Clique graphs Helly property Intersection graphs NP-complete problems |
| dc.description.none.fl_txt_mv |
A complete set of a graph G is a subset of vertices inducing a complete subgraph. A clique is a maximal complete set. Denote by C (G) the clique family of G. The clique graph of G, denoted by K (G), is the intersection graph of C (G). Say that G is a clique graph if there exists a graph H such that G = K (H). The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink in 1968, and a characterization was proposed by Roberts and Spencer in 1971. However, the time complexity of the problem of recognizing clique graphs is a long-standing open question. We prove that the clique graph recognition problem is NP-complete. Facultad de Ciencias Exactas |
| description |
A complete set of a graph G is a subset of vertices inducing a complete subgraph. A clique is a maximal complete set. Denote by C (G) the clique family of G. The clique graph of G, denoted by K (G), is the intersection graph of C (G). Say that G is a clique graph if there exists a graph H such that G = K (H). The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink in 1968, and a characterization was proposed by Roberts and Spencer in 1971. However, the time complexity of the problem of recognizing clique graphs is a long-standing open question. We prove that the clique graph recognition problem is NP-complete. |
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2009 |
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2009 |
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