Forbidden subgraphs and the König-Egerváry property

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...

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Detalhes bibliográficos
Autores: Bonomo, F., Dourado, M.C., Durán, G., Faria, L., Grippo, L.N., Safe, M.D.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:Argentina
Recursos:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
Repositorio:Biblioteca Digital (UBA-FCEN)
Idioma:inglés
OAI Identifier:paperaa:paper_0166218X_v161_n16-17_p2380_Bonomo
Acesso em linha:http://hdl.handle.net/20.500.12110/paper_0166218X_v161_n16-17_p2380_Bonomo
Access Level:acceso abierto
Palavra-chave:Edge-perfect graphs
Forbidden subgraphs
König-Egerváry graphs
König-Egerváry property
Maximum matching
Forbidden configurations
Forbidden subgraph characterizations
Matching numbers
Maximum matchings
Perfect matchings
Transversal number
Characterization
Graphic methods
Graph theory
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spelling Forbidden subgraphs and the König-Egerváry propertyBonomo, F.Dourado, M.C.Durán, G.Faria, L.Grippo, L.N.Safe, M.D.Edge-perfect graphsForbidden subgraphsKönig-Egerváry graphsKönig-Egerváry propertyMaximum matchingEdge-perfect graphsForbidden configurationsForbidden subgraph characterizationsForbidden subgraphsMatching numbersMaximum matchingsPerfect matchingsTransversal numberCharacterizationGraphic methodsGraph theoryThe 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. © 2013 Elsevier B.V. All rights reserved.Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Durán, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Grippo, L.N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Safe, M.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2013info: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_v161_n16-17_p2380_BonomoDiscrete Appl Math 2013;161(16-17):2380-2388reponame: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/ar2024-05-10T10:42:38Zpaperaa:paper_0166218X_v161_n16-17_p2380_BonomoInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962024-05-10 10:42:40.036Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
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, F.
Edge-perfect graphs
Forbidden subgraphs
König-Egerváry graphs
König-Egerváry property
Maximum matching
Edge-perfect graphs
Forbidden configurations
Forbidden subgraph characterizations
Forbidden subgraphs
Matching numbers
Maximum matchings
Perfect matchings
Transversal number
Characterization
Graphic methods
Graph theory
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, F.
Dourado, M.C.
Durán, G.
Faria, L.
Grippo, L.N.
Safe, M.D.
author Bonomo, F.
author_facet Bonomo, F.
Dourado, M.C.
Durán, G.
Faria, L.
Grippo, L.N.
Safe, M.D.
author_role author
author2 Dourado, M.C.
Durán, G.
Faria, L.
Grippo, L.N.
Safe, M.D.
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Edge-perfect graphs
Forbidden subgraphs
König-Egerváry graphs
König-Egerváry property
Maximum matching
Edge-perfect graphs
Forbidden configurations
Forbidden subgraph characterizations
Forbidden subgraphs
Matching numbers
Maximum matchings
Perfect matchings
Transversal number
Characterization
Graphic methods
Graph theory
topic Edge-perfect graphs
Forbidden subgraphs
König-Egerváry graphs
König-Egerváry property
Maximum matching
Edge-perfect graphs
Forbidden configurations
Forbidden subgraph characterizations
Forbidden subgraphs
Matching numbers
Maximum matchings
Perfect matchings
Transversal number
Characterization
Graphic methods
Graph theory
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. © 2013 Elsevier B.V. All rights reserved.
publishDate 2013
dc.date.none.fl_str_mv 2013
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_v161_n16-17_p2380_Bonomo
url http://hdl.handle.net/20.500.12110/paper_0166218X_v161_n16-17_p2380_Bonomo
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 2013;161(16-17):2380-2388
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (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 15,198674

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