Clique graph recognition is NP-complete

Autores
Alcón, Liliana Graciela; Faria, L.; Figueiredo, C. M. H. de; Gutiérrez, Marisa
Año de publicación
2006
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
A complete set of a graph G is a subset of V inducing a complete subgraph. A clique is a maximal complete set. Denote by the clique family of G. The clique graph of G, denoted by K(G), is the intersection graph of . 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. We prove that the clique graph recognition problem is NP-complete.
Facultad de Ciencias Exactas
Materia
Matemática
Planar graph
Complete graph
Intersection graph
Truth assignment
Nonempty intersection
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:10915/132535

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network_name_str SEDICI (UNLP)
spelling Clique graph recognition is NP-completeAlcón, Liliana GracielaFaria, L.Figueiredo, C. M. H. deGutiérrez, MarisaMatemáticaPlanar graphComplete graphIntersection graphTruth assignmentNonempty intersectionA complete set of a graph G is a subset of V inducing a complete subgraph. A clique is a maximal complete set. Denote by the clique family of G. The clique graph of G, denoted by K(G), is the intersection graph of . 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. We prove that the clique graph recognition problem is NP-complete.Facultad de Ciencias Exactas2006info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionObjeto de conferenciahttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdf269-277http://sedici.unlp.edu.ar/handle/10915/132535enginfo:eu-repo/semantics/altIdentifier/isbn/978-3-540-48382-3info:eu-repo/semantics/altIdentifier/issn/0302-9743info:eu-repo/semantics/altIdentifier/issn/1611-3349info:eu-repo/semantics/altIdentifier/doi/10.1007/11917496_24info: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:UNLP2025-09-29T11:32:12Zoai:sedici.unlp.edu.ar:10915/132535Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:32:13.118SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Clique graph recognition is NP-complete
title Clique graph recognition is NP-complete
spellingShingle Clique graph recognition is NP-complete
Alcón, Liliana Graciela
Matemática
Planar graph
Complete graph
Intersection graph
Truth assignment
Nonempty intersection
title_short Clique graph recognition is NP-complete
title_full Clique graph recognition is NP-complete
title_fullStr Clique graph recognition is NP-complete
title_full_unstemmed Clique graph recognition is NP-complete
title_sort Clique graph recognition is NP-complete
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Faria, L.
Figueiredo, C. M. H. de
Gutiérrez, Marisa
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Faria, L.
Figueiredo, C. M. H. de
Gutiérrez, Marisa
author_role author
author2 Faria, L.
Figueiredo, C. M. H. de
Gutiérrez, Marisa
author2_role author
author
author
dc.subject.none.fl_str_mv Matemática
Planar graph
Complete graph
Intersection graph
Truth assignment
Nonempty intersection
topic Matemática
Planar graph
Complete graph
Intersection graph
Truth assignment
Nonempty intersection
dc.description.none.fl_txt_mv A complete set of a graph G is a subset of V inducing a complete subgraph. A clique is a maximal complete set. Denote by the clique family of G. The clique graph of G, denoted by K(G), is the intersection graph of . 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. 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 V inducing a complete subgraph. A clique is a maximal complete set. Denote by the clique family of G. The clique graph of G, denoted by K(G), is the intersection graph of . 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. We prove that the clique graph recognition problem is NP-complete.
publishDate 2006
dc.date.none.fl_str_mv 2006
dc.type.none.fl_str_mv info:eu-repo/semantics/conferenceObject
info:eu-repo/semantics/publishedVersion
Objeto de conferencia
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dc.language.none.fl_str_mv eng
language eng
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info:eu-repo/semantics/altIdentifier/issn/0302-9743
info:eu-repo/semantics/altIdentifier/issn/1611-3349
info:eu-repo/semantics/altIdentifier/doi/10.1007/11917496_24
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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269-277
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