The complexity of clique graph recognition
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...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2009 |
| País: | Argentina |
| Recursos: | Universidad Nacional de La Plata |
| Repositório: | SEDICI (UNLP) |
| Idioma: | inglês |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/82662 |
| Acesso em linha: | http://sedici.unlp.edu.ar/handle/10915/82662 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Matemática Clique graphs Helly property Intersection graphs NP-complete problems |
| Resumo: | 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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