Forbidden subgraphs and the König–Egerváry property

Autores
Bonomo, Flavia; Dourado, Mitre C.; Duran, Guillermo Alfredo; Faria, Luerbio; Grippo, Luciano Norberto; Safe, Martin Dario
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The matching number of a graph is the maximum size of a set of vertex-disjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the König-Egerváry property if its matching number equals its transversal number. Lovász proved a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs within graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovász´s result to a characterization of all graphs having the König-Egerváry property in terms of forbidden configurations (which are certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. Using our characterization of graphs with the König-Egerváry property, we also prove a forbidden subgraph characterization for the class of edge-perfect graphs.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dourado, Mitre C.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Duran, Guillermo Alfredo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Chile; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Faria, Luerbio. Universidade do Estado do Rio de Janeiro; Brasil
Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Edge-Perfect Graphs
Forbidden Subgraphs
König-Egerváry Property
König-Egerváry Graphs
Maximum Matching
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18841
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18841
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Forbidden subgraphs and the König–Egerváry propertyBonomo, FlaviaDourado, Mitre C.Duran, Guillermo AlfredoFaria, LuerbioGrippo, Luciano NorbertoSafe, Martin DarioEdge-Perfect GraphsForbidden SubgraphsKönig-Egerváry PropertyKönig-Egerváry GraphsMaximum Matchinghttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1The matching number of a graph is the maximum size of a set of vertex-disjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the König-Egerváry property if its matching number equals its transversal number. Lovász proved a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs within graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovász´s result to a characterization of all graphs having the König-Egerváry property in terms of forbidden configurations (which are certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. Using our characterization of graphs with the König-Egerváry property, we also prove a forbidden subgraph characterization for the class of edge-perfect graphs.Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dourado, Mitre C.. Universidade Federal do Rio de Janeiro; BrasilFil: Duran, Guillermo Alfredo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Chile; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Faria, Luerbio. Universidade do Estado do Rio de Janeiro; BrasilFil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2013-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18841Bonomo, Flavia; Dourado, Mitre C.; Duran, Guillermo Alfredo; Faria, Luerbio; Grippo, Luciano Norberto; et al.; Forbidden subgraphs and the König–Egerváry property; Elsevier Science; Discrete Applied Mathematics; 161; 16-17; 11-2013; 2380-23880166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2013.04.020info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0166218X13002072info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:22:17Zoai:ri.conicet.gov.ar:11336/18841instacron: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:34982025-09-10 13:22:17.78CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Forbidden subgraphs and the König–Egerváry property
title Forbidden subgraphs and the König–Egerváry property
spellingShingle Forbidden subgraphs and the König–Egerváry property
Bonomo, Flavia
Edge-Perfect Graphs
Forbidden Subgraphs
König-Egerváry Property
König-Egerváry Graphs
Maximum Matching
title_short Forbidden subgraphs and the König–Egerváry property
title_full Forbidden subgraphs and the König–Egerváry property
title_fullStr Forbidden subgraphs and the König–Egerváry property
title_full_unstemmed Forbidden subgraphs and the König–Egerváry property
title_sort Forbidden subgraphs and the König–Egerváry property
dc.creator.none.fl_str_mv Bonomo, Flavia
Dourado, Mitre C.
Duran, Guillermo Alfredo
Faria, Luerbio
Grippo, Luciano Norberto
Safe, Martin Dario
author Bonomo, Flavia
author_facet Bonomo, Flavia
Dourado, Mitre C.
Duran, Guillermo Alfredo
Faria, Luerbio
Grippo, Luciano Norberto
Safe, Martin Dario
author_role author
author2 Dourado, Mitre C.
Duran, Guillermo Alfredo
Faria, Luerbio
Grippo, Luciano Norberto
Safe, Martin Dario
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Edge-Perfect Graphs
Forbidden Subgraphs
König-Egerváry Property
König-Egerváry Graphs
Maximum Matching
topic Edge-Perfect Graphs
Forbidden Subgraphs
König-Egerváry Property
König-Egerváry Graphs
Maximum Matching
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The matching number of a graph is the maximum size of a set of vertex-disjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the König-Egerváry property if its matching number equals its transversal number. Lovász proved a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs within graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovász´s result to a characterization of all graphs having the König-Egerváry property in terms of forbidden configurations (which are certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. Using our characterization of graphs with the König-Egerváry property, we also prove a forbidden subgraph characterization for the class of edge-perfect graphs.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dourado, Mitre C.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Duran, Guillermo Alfredo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Chile; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Faria, Luerbio. Universidade do Estado do Rio de Janeiro; Brasil
Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description The matching number of a graph is the maximum size of a set of vertex-disjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the König-Egerváry property if its matching number equals its transversal number. Lovász proved a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs within graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovász´s result to a characterization of all graphs having the König-Egerváry property in terms of forbidden configurations (which are certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. Using our characterization of graphs with the König-Egerváry property, we also prove a forbidden subgraph characterization for the class of edge-perfect graphs.
publishDate 2013
dc.date.none.fl_str_mv 2013-11
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/11336/18841
Bonomo, Flavia; Dourado, Mitre C.; Duran, Guillermo Alfredo; Faria, Luerbio; Grippo, Luciano Norberto; et al.; Forbidden subgraphs and the König–Egerváry property; Elsevier Science; Discrete Applied Mathematics; 161; 16-17; 11-2013; 2380-2388
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18841
identifier_str_mv Bonomo, Flavia; Dourado, Mitre C.; Duran, Guillermo Alfredo; Faria, Luerbio; Grippo, Luciano Norberto; et al.; Forbidden subgraphs and the König–Egerváry property; Elsevier Science; Discrete Applied Mathematics; 161; 16-17; 11-2013; 2380-2388
0166-218X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2013.04.020
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0166218X13002072
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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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score 12.48226

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