Covergence and divergence of the iterated biclique graph
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...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/15646 |
| Acesso em linha: | http://hdl.handle.net/11336/15646 |
| Access Level: | acceso abierto |
| Palavra-chave: | Bicliques Biclique Graphs Clique Graphs Divergent Graphs Iterated Graph Operators Graph Dynamics https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
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Covergence and divergence of the iterated biclique graphGroshaus, Marina EstherMontero, Leandro PedroBicliquesBiclique GraphsClique GraphsDivergent GraphsIterated Graph OperatorsGraph Dynamicshttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1A 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.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: Montero, Leandro Pedro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaWiley2013-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15646Groshaus, Marina Esther; Montero, Leandro Pedro; Covergence and divergence of the iterated biclique graph; Wiley; Journal Of Graph Theory; 73; 2; 6-2013; 181-1900364-9024enginfo:eu-repo/semantics/altIdentifier/doi/10.1002/jgt.21666info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1002/jgt.21666/abstractinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:34:02Zoai:ri.conicet.gov.ar:11336/15646instacron: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:34982024-05-08 13:34:02.82CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Covergence and divergence of the iterated biclique graph |
| title |
Covergence and divergence of the iterated biclique graph |
| spellingShingle |
Covergence and divergence of the iterated biclique graph Groshaus, Marina Esther Bicliques Biclique Graphs Clique Graphs Divergent Graphs Iterated Graph Operators Graph Dynamics https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| title_short |
Covergence and divergence of the iterated biclique graph |
| title_full |
Covergence and divergence of the iterated biclique graph |
| title_fullStr |
Covergence and divergence of the iterated biclique graph |
| title_full_unstemmed |
Covergence and divergence of the iterated biclique graph |
| title_sort |
Covergence and divergence of the iterated biclique graph |
| dc.creator.none.fl_str_mv |
Groshaus, Marina Esther Montero, Leandro Pedro |
| author |
Groshaus, Marina Esther |
| author_facet |
Groshaus, Marina Esther Montero, Leandro Pedro |
| author_role |
author |
| author2 |
Montero, Leandro Pedro |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Bicliques Biclique Graphs Clique Graphs Divergent Graphs Iterated Graph Operators Graph Dynamics https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| topic |
Bicliques Biclique Graphs Clique Graphs Divergent Graphs Iterated Graph Operators Graph Dynamics https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| description |
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. |
| publishDate |
2013 |
| dc.date.none.fl_str_mv |
2013-06 |
| 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/11336/15646 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 0364-9024 |
| url |
http://hdl.handle.net/11336/15646 |
| identifier_str_mv |
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 0364-9024 |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1002/jgt.21666 info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1002/jgt.21666/abstract |
| 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 |
Wiley |
| publisher.none.fl_str_mv |
Wiley |
| dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
| instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
| reponame_str |
CONICET Digital (CONICET) |
| collection |
CONICET Digital (CONICET) |
| 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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1799194674331648000 |
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15.812455 |