On edge-sets of bicliques in graphs

Autores
Groshaus, M.; Hell, P.; Stacho, J.
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edge-biclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) by means of a single forbidden induced obstruction, the triangular prism. Using this result, we characterize graphs whose edge-biclique hypergraph is Helly and provide a polynomial time recognition algorithm. We further study a hereditary version of this property and show that it also admits polynomial time recognition, and, in fact, is characterized by a finite set of forbidden induced subgraphs. We conclude by describing some interesting properties of the 2-section graph of the edge-biclique hypergraph. © 2011 Elsevier B.V. All rights reserved.
Fil:Groshaus, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
Discrete Appl Math 2012;160(18):2698-2708
Materia
2-section
Biclique
Clique graph
Conformal
Helly
Hypergraph
Intersection graph
2-section
Biclique
Clique graphs
Conformal
Helly
Hypergraph
Intersection graph
Combinatorial mathematics
Mathematical techniques
Polynomial approximation
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_0166218X_v160_n18_p2698_Groshaus
Acceder
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oai_identifier_str paperaa:paper_0166218X_v160_n18_p2698_Groshaus
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling On edge-sets of bicliques in graphsGroshaus, M.Hell, P.Stacho, J.2-sectionBicliqueClique graphConformalHellyHypergraphIntersection graph2-sectionBicliqueClique graphsConformalHellyHypergraphIntersection graphCombinatorial mathematicsMathematical techniquesPolynomial approximationA biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edge-biclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) by means of a single forbidden induced obstruction, the triangular prism. Using this result, we characterize graphs whose edge-biclique hypergraph is Helly and provide a polynomial time recognition algorithm. We further study a hereditary version of this property and show that it also admits polynomial time recognition, and, in fact, is characterized by a finite set of forbidden induced subgraphs. We conclude by describing some interesting properties of the 2-section graph of the edge-biclique hypergraph. © 2011 Elsevier B.V. All rights reserved.Fil:Groshaus, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0166218X_v160_n18_p2698_GroshausDiscrete Appl Math 2012;160(18):2698-2708reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-16T09:30:10Zpaperaa:paper_0166218X_v160_n18_p2698_GroshausInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-16 09:30:12.057Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv On edge-sets of bicliques in graphs
title On edge-sets of bicliques in graphs
spellingShingle On edge-sets of bicliques in graphs
Groshaus, M.
2-section
Biclique
Clique graph
Conformal
Helly
Hypergraph
Intersection graph
2-section
Biclique
Clique graphs
Conformal
Helly
Hypergraph
Intersection graph
Combinatorial mathematics
Mathematical techniques
Polynomial approximation
title_short On edge-sets of bicliques in graphs
title_full On edge-sets of bicliques in graphs
title_fullStr On edge-sets of bicliques in graphs
title_full_unstemmed On edge-sets of bicliques in graphs
title_sort On edge-sets of bicliques in graphs
dc.creator.none.fl_str_mv Groshaus, M.
Hell, P.
Stacho, J.
author Groshaus, M.
author_facet Groshaus, M.
Hell, P.
Stacho, J.
author_role author
author2 Hell, P.
Stacho, J.
author2_role author
author
dc.subject.none.fl_str_mv 2-section
Biclique
Clique graph
Conformal
Helly
Hypergraph
Intersection graph
2-section
Biclique
Clique graphs
Conformal
Helly
Hypergraph
Intersection graph
Combinatorial mathematics
Mathematical techniques
Polynomial approximation
topic 2-section
Biclique
Clique graph
Conformal
Helly
Hypergraph
Intersection graph
2-section
Biclique
Clique graphs
Conformal
Helly
Hypergraph
Intersection graph
Combinatorial mathematics
Mathematical techniques
Polynomial approximation
dc.description.none.fl_txt_mv A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edge-biclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) by means of a single forbidden induced obstruction, the triangular prism. Using this result, we characterize graphs whose edge-biclique hypergraph is Helly and provide a polynomial time recognition algorithm. We further study a hereditary version of this property and show that it also admits polynomial time recognition, and, in fact, is characterized by a finite set of forbidden induced subgraphs. We conclude by describing some interesting properties of the 2-section graph of the edge-biclique hypergraph. © 2011 Elsevier B.V. All rights reserved.
Fil:Groshaus, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edge-biclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) by means of a single forbidden induced obstruction, the triangular prism. Using this result, we characterize graphs whose edge-biclique hypergraph is Helly and provide a polynomial time recognition algorithm. We further study a hereditary version of this property and show that it also admits polynomial time recognition, and, in fact, is characterized by a finite set of forbidden induced subgraphs. We conclude by describing some interesting properties of the 2-section graph of the edge-biclique hypergraph. © 2011 Elsevier B.V. All rights reserved.
publishDate 2012
dc.date.none.fl_str_mv 2012
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/20.500.12110/paper_0166218X_v160_n18_p2698_Groshaus
url http://hdl.handle.net/20.500.12110/paper_0166218X_v160_n18_p2698_Groshaus
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Discrete Appl Math 2012;160(18):2698-2708
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 12.712165

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