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...

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Detalles Bibliográficos
Autores principales: Alcón, Liliana Graciela, Gutiérrez, Marisa
Formato: Articulo
Lenguaje:Inglés
Publicado: 2004
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Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/83260
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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.