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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
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
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
Volumen:63
Número:1
Página de inicio:1
Página de fin:16
DOI: http://dx.doi.org/10.1002/jgt.20442
Título revista:Journal of Graph Theory
Título revista abreviado:J. Graph Theory
ISSN:03649024
CODEN:JGTHD
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