Abstract:
A biclique of a graph G is a maximal induced complete bipar tite subgraph of G. Given a graph G, the biclique matrix of G is a {0,1, -1} matrix having one row for each biclique and one column for each vertex of G, and such that a pair of 1, -1 entries in a same row corresponds exactly to adjacent vertices in the corresponding biclique. We describe a characterization of biclique matrices, in similar terms as those employed in Gilmore's characterization of clique matrices. On the other hand, the biclique graph of a graph is the intersection graph of the bicliques of G. Using the concept of biclique matrices, we describe a Krausz-type char acterization of biclique graphs. Finally, we show that every induced P3 of a biclique graph must be included in a diamond or in a 3-fan and we also characterize biclique graphs of bipartite graphs. © 2009 Wiley Periodicals, inc.
Registro:
Documento: |
Artículo
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Título: | Biclique graphs and biclique matrices |
Autor: | Groshaus, M.; Szwarcfiter, J.L. |
Filiación: | Departamento de Computación, Universidad de Buenos Aires, Buenos Aires, Argentina Instituto de Matemáticance and Coppe, Universidade Federaldo do Rio de Janeiro, Rio de Janeiro, Brazil
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Palabras clave: | Biclique graphs; Bicliques; Bipartite matrices; Clique graphs; Cliques; Adjacent vertices; Biclique; Bipartite graphs; Clique graphs; Graph G; Intersection graph; matrix; Subgraphs |
Año: | 2010
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Volumen: | 63
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Número: | 1
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Página de inicio: | 1
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Página de fin: | 16
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DOI: |
http://dx.doi.org/10.1002/jgt.20442 |
Título revista: | Journal of Graph Theory
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Título revista abreviado: | J. Graph Theory
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ISSN: | 03649024
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CODEN: | JGTHD
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03649024_v63_n1_p1_Groshaus |
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Citas:
---------- APA ----------
Groshaus, M. & Szwarcfiter, J.L.
(2010)
. Biclique graphs and biclique matrices. Journal of Graph Theory, 63(1), 1-16.
http://dx.doi.org/10.1002/jgt.20442---------- CHICAGO ----------
Groshaus, M., Szwarcfiter, J.L.
"Biclique graphs and biclique matrices"
. Journal of Graph Theory 63, no. 1
(2010) : 1-16.
http://dx.doi.org/10.1002/jgt.20442---------- MLA ----------
Groshaus, M., Szwarcfiter, J.L.
"Biclique graphs and biclique matrices"
. Journal of Graph Theory, vol. 63, no. 1, 2010, pp. 1-16.
http://dx.doi.org/10.1002/jgt.20442---------- VANCOUVER ----------
Groshaus, M., Szwarcfiter, J.L. Biclique graphs and biclique matrices. J. Graph Theory. 2010;63(1):1-16.
http://dx.doi.org/10.1002/jgt.20442