Clique-critical graphs: Maximum size and recognition
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...
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2006
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/83201 |
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| Sumario: | 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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