Cliques and extended triangles : A necessary condition for planar clique graphs
By generalizing the idea of extended triangle of a graph, we succeed in obtaining a common framework for the result of Roberts and Spencer about clique graphs and the one of Szwarcfiter about Helly graphs. We characterize Helly and 3-Helly planar graphs using extended triangles. We prove that if a p...
Guardado en:
| Autores principales: | , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2004
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/83260 |
| Aporte de: |
| Sumario: | By generalizing the idea of extended triangle of a graph, we succeed in obtaining a common framework for the result of Roberts and Spencer about clique graphs and the one of Szwarcfiter about Helly graphs. We characterize Helly and 3-Helly planar graphs using extended triangles. We prove that if a planar graph G is a clique graph, then every extended triangle of G must be a clique graph. Finally, we show the extended triangles of a planar graph which are clique graphs. Any one of the obtained characterizations are tested in O(n2) time. |
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