Clique-perfectness of complements of line graphs

Autores
Bonomo, Flavia; Duran, Guillermo Alfredo; Safe, Martin Dario; Wagler, Annegret Katrin
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A graph is clique-perfect if the maximum number of pairwise disjoint maximal cliques equals the minimum number of vertices intersecting all maximal cliques for each induced subgraph. In this work, we give necessary and sufficient conditions for the complement of a line graph to be clique-perfect and an O(n 2 )-time algorithm to recognize such graphs. These results follow from a characterization and a linear-time recognition algorithm for matching-perfect graphs, which we introduce as graphs where the maximum number of pairwise edge-disjoint maximal matchings equals the minimum number of edges intersecting all maximal matchings for each subgraph. Thereby, we completely describe the linear and circular structure of the graphs containing no bipartite claw, from which we derive a structure theorem for all those graphs containing no bipartite claw that are Class 2 with respect to edge-coloring.
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: 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: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Wagler, Annegret Katrin. Universite Blaise Pascal; Francia
Materia
Clique-Perfect Graphs
Edge-Coloring
Line Graphs
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:11336/18898

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spelling Clique-perfectness of complements of line graphsBonomo, FlaviaDuran, Guillermo AlfredoSafe, Martin DarioWagler, Annegret KatrinClique-Perfect GraphsEdge-ColoringLine GraphsMatchinghttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1A graph is clique-perfect if the maximum number of pairwise disjoint maximal cliques equals the minimum number of vertices intersecting all maximal cliques for each induced subgraph. In this work, we give necessary and sufficient conditions for the complement of a line graph to be clique-perfect and an O(n 2 )-time algorithm to recognize such graphs. These results follow from a characterization and a linear-time recognition algorithm for matching-perfect graphs, which we introduce as graphs where the maximum number of pairwise edge-disjoint maximal matchings equals the minimum number of edges intersecting all maximal matchings for each subgraph. Thereby, we completely describe the linear and circular structure of the graphs containing no bipartite claw, from which we derive a structure theorem for all those graphs containing no bipartite claw that are Class 2 with respect to edge-coloring.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: 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: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Wagler, Annegret Katrin. Universite Blaise Pascal; FranciaElsevier Science2015-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18898Bonomo, Flavia; Duran, Guillermo Alfredo; Safe, Martin Dario; Wagler, Annegret Katrin; Clique-perfectness of complements of line graphs; Elsevier Science; Discrete Applied Mathematics; 186; 5-2015; 19-440166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2015.01.012info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0166218X1500013Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:23:48Zoai:ri.conicet.gov.ar:11336/18898instacron: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:34982025-10-15 15:23:48.52CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Clique-perfectness of complements of line graphs
title Clique-perfectness of complements of line graphs
spellingShingle Clique-perfectness of complements of line graphs
Bonomo, Flavia
Clique-Perfect Graphs
Edge-Coloring
Line Graphs
Matching
title_short Clique-perfectness of complements of line graphs
title_full Clique-perfectness of complements of line graphs
title_fullStr Clique-perfectness of complements of line graphs
title_full_unstemmed Clique-perfectness of complements of line graphs
title_sort Clique-perfectness of complements of line graphs
dc.creator.none.fl_str_mv Bonomo, Flavia
Duran, Guillermo Alfredo
Safe, Martin Dario
Wagler, Annegret Katrin
author Bonomo, Flavia
author_facet Bonomo, Flavia
Duran, Guillermo Alfredo
Safe, Martin Dario
Wagler, Annegret Katrin
author_role author
author2 Duran, Guillermo Alfredo
Safe, Martin Dario
Wagler, Annegret Katrin
author2_role author
author
author
dc.subject.none.fl_str_mv Clique-Perfect Graphs
Edge-Coloring
Line Graphs
Matching
topic Clique-Perfect Graphs
Edge-Coloring
Line Graphs
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 A graph is clique-perfect if the maximum number of pairwise disjoint maximal cliques equals the minimum number of vertices intersecting all maximal cliques for each induced subgraph. In this work, we give necessary and sufficient conditions for the complement of a line graph to be clique-perfect and an O(n 2 )-time algorithm to recognize such graphs. These results follow from a characterization and a linear-time recognition algorithm for matching-perfect graphs, which we introduce as graphs where the maximum number of pairwise edge-disjoint maximal matchings equals the minimum number of edges intersecting all maximal matchings for each subgraph. Thereby, we completely describe the linear and circular structure of the graphs containing no bipartite claw, from which we derive a structure theorem for all those graphs containing no bipartite claw that are Class 2 with respect to edge-coloring.
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: 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: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Wagler, Annegret Katrin. Universite Blaise Pascal; Francia
description A graph is clique-perfect if the maximum number of pairwise disjoint maximal cliques equals the minimum number of vertices intersecting all maximal cliques for each induced subgraph. In this work, we give necessary and sufficient conditions for the complement of a line graph to be clique-perfect and an O(n 2 )-time algorithm to recognize such graphs. These results follow from a characterization and a linear-time recognition algorithm for matching-perfect graphs, which we introduce as graphs where the maximum number of pairwise edge-disjoint maximal matchings equals the minimum number of edges intersecting all maximal matchings for each subgraph. Thereby, we completely describe the linear and circular structure of the graphs containing no bipartite claw, from which we derive a structure theorem for all those graphs containing no bipartite claw that are Class 2 with respect to edge-coloring.
publishDate 2015
dc.date.none.fl_str_mv 2015-05
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/11336/18898
Bonomo, Flavia; Duran, Guillermo Alfredo; Safe, Martin Dario; Wagler, Annegret Katrin; Clique-perfectness of complements of line graphs; Elsevier Science; Discrete Applied Mathematics; 186; 5-2015; 19-44
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18898
identifier_str_mv Bonomo, Flavia; Duran, Guillermo Alfredo; Safe, Martin Dario; Wagler, Annegret Katrin; Clique-perfectness of complements of line graphs; Elsevier Science; Discrete Applied Mathematics; 186; 5-2015; 19-44
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.2015.01.012
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0166218X1500013X
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
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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