Artículo
Covergence and divergence of the iterated biclique graph
Fecha de publicación:
06/2013
Editorial:
Wiley
Revista:
Journal Of Graph Theory
ISSN:
0364-9024
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph of G, denoted by KB(G), is the intersection graph of the bicliques of G. We say that a graph G diverges (or converges or is periodic) under an operator F whenever limk→∞ |V (F k (G))| = ∞ (limk→∞ F k (G) = F m(G) for some m, or F k (G) = F k+s(G) for some k and s ≥ 2, respectively). Given a graph G, the iterated biclique graph of G, denoted by KBk (G), is the graph obtained by applying the biclique operator k successive times to G. In this article, we study the iterated biclique graph of G. In particular, we classify the different behaviors of KBk (G) when the number of iterations k grows to infinity. That is, we prove that a graph either diverges or converges under the biclique operator. We give a forbidden structure characterization of convergent graphs, which yield a polynomial time algorithm to decide if a given graph diverges or converges. This is in sharp contrast with the situsation for the better known clique operator, where it is not even known if the corresponding problem is decidable.
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(OCA CIUDAD UNIVERSITARIA)
Articulos de OFICINA DE COORDINACION ADMINISTRATIVA CIUDAD UNIVERSITARIA
Articulos de OFICINA DE COORDINACION ADMINISTRATIVA CIUDAD UNIVERSITARIA
Citación
Groshaus, Marina Esther; Montero, Leandro Pedro; Covergence and divergence of the iterated biclique graph; Wiley; Journal Of Graph Theory; 73; 2; 6-2013; 181-190
Compartir
Altmétricas
Items relacionados
Mostrando titulos relacionados por título, autor y tema.
-
Bonomo-Braberman, Flavia; Durán, Guillermo; Safe, Martin Dario ; Wagler, Annegret K. (Elsevier Science, 2020-07-15)
-
de Caria, Pablo Jesús ; Gutierrez, Marisa (Elsevier Science, 2016-09)
-
Bonomo, Flavia ; Duran, Guillermo Alfredo ; Safe, Martin Dario ; Wagler, Annegret Katrin (Discrete Mathematics and Theoretical Computer Science, 2014-03)