Biclique graphs and biclique matrices
- Autores
- Groshaus, Marina Esther; Szwarcfiter, Jayme L.
- Año de publicación
- 2010
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
Fil: Groshaus, Marina Esther. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil - Materia
-
Biclique Graphs
Bicliques
Bipartite Matrices
Clique Graphs
Cliques - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/68007
Ver los metadatos del registro completo
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Biclique graphs and biclique matricesGroshaus, Marina EstherSzwarcfiter, Jayme L.Biclique GraphsBicliquesBipartite MatricesClique GraphsCliqueshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A 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.Fil: Groshaus, Marina Esther. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; BrasilJohn Wiley & Sons Inc2010-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/68007Groshaus, Marina Esther; Szwarcfiter, Jayme L.; Biclique graphs and biclique matrices; John Wiley & Sons Inc; Journal of Graph Theory; 63; 1; 1-2010; 1-160364-9024CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1002/jgt.20442info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/jgt.20442info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:01:27Zoai:ri.conicet.gov.ar:11336/68007instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:01:27.782CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Biclique graphs and biclique matrices |
title |
Biclique graphs and biclique matrices |
spellingShingle |
Biclique graphs and biclique matrices Groshaus, Marina Esther Biclique Graphs Bicliques Bipartite Matrices Clique Graphs Cliques |
title_short |
Biclique graphs and biclique matrices |
title_full |
Biclique graphs and biclique matrices |
title_fullStr |
Biclique graphs and biclique matrices |
title_full_unstemmed |
Biclique graphs and biclique matrices |
title_sort |
Biclique graphs and biclique matrices |
dc.creator.none.fl_str_mv |
Groshaus, Marina Esther Szwarcfiter, Jayme L. |
author |
Groshaus, Marina Esther |
author_facet |
Groshaus, Marina Esther Szwarcfiter, Jayme L. |
author_role |
author |
author2 |
Szwarcfiter, Jayme L. |
author2_role |
author |
dc.subject.none.fl_str_mv |
Biclique Graphs Bicliques Bipartite Matrices Clique Graphs Cliques |
topic |
Biclique Graphs Bicliques Bipartite Matrices Clique Graphs Cliques |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
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. Fil: Groshaus, Marina Esther. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil |
description |
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. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010-01 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/68007 Groshaus, Marina Esther; Szwarcfiter, Jayme L.; Biclique graphs and biclique matrices; John Wiley & Sons Inc; Journal of Graph Theory; 63; 1; 1-2010; 1-16 0364-9024 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/68007 |
identifier_str_mv |
Groshaus, Marina Esther; Szwarcfiter, Jayme L.; Biclique graphs and biclique matrices; John Wiley & Sons Inc; Journal of Graph Theory; 63; 1; 1-2010; 1-16 0364-9024 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1002/jgt.20442 info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/jgt.20442 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
John Wiley & Sons Inc |
publisher.none.fl_str_mv |
John Wiley & Sons Inc |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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1842269695633260544 |
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13.13397 |