Clique-critical graphs: Maximum size and recognition
- Autores
- Alcón, Liliana Graciela
- Año de publicación
- 2006
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- The clique graph of G, K (G), is the intersection graph of the family of cliques (maximal complete sets) of G. Clique-critical graphs were defined as those whose clique graph changes whenever a vertex is removed. We prove that if G has m edges then any clique-critical graph in K-1 (G) has at most 2m vertices, which solves a question posed by Escalante and Toft [On clique-critical graphs, J. Combin. Theory B 17 (1974) 170-182]. The proof is based on a restatement of their characterization of clique-critical graphs. Moreover, the bound is sharp. We also show that the problem of recognizing clique-critical graphs is NP-complete.
Facultad de Ciencias Exactas - Materia
-
Ciencias Exactas
Clique graphs
Clique-critical 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:10915/83201
Ver los metadatos del registro completo
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Clique-critical graphs: Maximum size and recognitionAlcón, Liliana GracielaCiencias ExactasClique graphsClique-critical graphsNP-complete problemsThe clique graph of G, K (G), is the intersection graph of the family of cliques (maximal complete sets) of G. Clique-critical graphs were defined as those whose clique graph changes whenever a vertex is removed. We prove that if G has m edges then any clique-critical graph in K<SUB>-1</SUB> (G) has at most 2m vertices, which solves a question posed by Escalante and Toft [On clique-critical graphs, J. Combin. Theory B 17 (1974) 170-182]. The proof is based on a restatement of their characterization of clique-critical graphs. Moreover, the bound is sharp. We also show that the problem of recognizing clique-critical graphs is NP-complete.Facultad de Ciencias Exactas2006info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1799-1802http://sedici.unlp.edu.ar/handle/10915/83201enginfo:eu-repo/semantics/altIdentifier/issn/0166-218Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2006.03.024info: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:UNLP2025-09-03T10:48:01Zoai:sedici.unlp.edu.ar:10915/83201Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 10:48:01.874SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
Clique-critical graphs: Maximum size and recognition |
| title |
Clique-critical graphs: Maximum size and recognition |
| spellingShingle |
Clique-critical graphs: Maximum size and recognition Alcón, Liliana Graciela Ciencias Exactas Clique graphs Clique-critical graphs NP-complete problems |
| title_short |
Clique-critical graphs: Maximum size and recognition |
| title_full |
Clique-critical graphs: Maximum size and recognition |
| title_fullStr |
Clique-critical graphs: Maximum size and recognition |
| title_full_unstemmed |
Clique-critical graphs: Maximum size and recognition |
| title_sort |
Clique-critical graphs: Maximum size and recognition |
| dc.creator.none.fl_str_mv |
Alcón, Liliana Graciela |
| author |
Alcón, Liliana Graciela |
| author_facet |
Alcón, Liliana Graciela |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Ciencias Exactas Clique graphs Clique-critical graphs NP-complete problems |
| topic |
Ciencias Exactas Clique graphs Clique-critical graphs NP-complete problems |
| dc.description.none.fl_txt_mv |
The clique graph of G, K (G), is the intersection graph of the family of cliques (maximal complete sets) of G. Clique-critical graphs were defined as those whose clique graph changes whenever a vertex is removed. We prove that if G has m edges then any clique-critical graph in K<SUB>-1</SUB> (G) has at most 2m vertices, which solves a question posed by Escalante and Toft [On clique-critical graphs, J. Combin. Theory B 17 (1974) 170-182]. The proof is based on a restatement of their characterization of clique-critical graphs. Moreover, the bound is sharp. We also show that the problem of recognizing clique-critical graphs is NP-complete. Facultad de Ciencias Exactas |
| description |
The clique graph of G, K (G), is the intersection graph of the family of cliques (maximal complete sets) of G. Clique-critical graphs were defined as those whose clique graph changes whenever a vertex is removed. We prove that if G has m edges then any clique-critical graph in K<SUB>-1</SUB> (G) has at most 2m vertices, which solves a question posed by Escalante and Toft [On clique-critical graphs, J. Combin. Theory B 17 (1974) 170-182]. The proof is based on a restatement of their characterization of clique-critical graphs. Moreover, the bound is sharp. We also show that the problem of recognizing clique-critical graphs is NP-complete. |
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2006 |
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2006 |
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