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...
Guardado en:
| Autores principales: | , , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2009
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/82662 |
| Aporte de: |
| Sumario: | 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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