Strong cliques and equistability of EPT graphs

Autores
Alcón, Liliana Graciela; Gutierrez, Marisa; Kovács, István; Milanič, Martin; Rizzi, Romeo
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we characterize the equistable graphs within the class of EPT graphs, the edge-intersection graphs of paths in a tree. This result generalizes a previously known characterization of equistable line graphs. Our approach is based on the combinatorial features of triangle graphs and general partition graphs. We also show that, in EPT graphs, testing whether a given clique is strong is co-NP-complete. We obtain this hardness result by first showing hardness of the problem of determining whether a given graph has a maximal matching disjoint from a given edge cut. As a positive result, we prove that the problem of testing whether a given clique is strong is polynomial in the class of local EPT graphs, which are defined as the edge intersection graphs of paths in a star and are known to coincide with the line graphs of multigraphs.
Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Kovács, István. University of Primorska; Eslovenia
Fil: Milanič, Martin. University of Primorska; Eslovenia
Fil: Rizzi, Romeo. Universita di Verona; Italia
Materia
Ept Graph
Equistable Graph
General Partition Graph
Strong Clique
Triangle Condition
Triangle Graph
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:11336/54193
Acceder
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spelling Strong cliques and equistability of EPT graphsAlcón, Liliana GracielaGutierrez, MarisaKovács, IstvánMilanič, MartinRizzi, RomeoEpt GraphEquistable GraphGeneral Partition GraphStrong CliqueTriangle ConditionTriangle Graphhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we characterize the equistable graphs within the class of EPT graphs, the edge-intersection graphs of paths in a tree. This result generalizes a previously known characterization of equistable line graphs. Our approach is based on the combinatorial features of triangle graphs and general partition graphs. We also show that, in EPT graphs, testing whether a given clique is strong is co-NP-complete. We obtain this hardness result by first showing hardness of the problem of determining whether a given graph has a maximal matching disjoint from a given edge cut. As a positive result, we prove that the problem of testing whether a given clique is strong is polynomial in the class of local EPT graphs, which are defined as the edge intersection graphs of paths in a star and are known to coincide with the line graphs of multigraphs.Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Kovács, István. University of Primorska; EsloveniaFil: Milanič, Martin. University of Primorska; EsloveniaFil: Rizzi, Romeo. Universita di Verona; ItaliaElsevier Science2016-04info: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/11336/54193Alcón, Liliana Graciela; Gutierrez, Marisa; Kovács, István; Milanič, Martin; Rizzi, Romeo; Strong cliques and equistability of EPT graphs; Elsevier Science; Discrete Applied Mathematics; 203; 4-2016; 13-250166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X15004771info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2015.09.016info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:12:13Zoai:ri.conicet.gov.ar:11336/54193instacron: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:34982025-09-29 10:12:13.362CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Strong cliques and equistability of EPT graphs
title Strong cliques and equistability of EPT graphs
spellingShingle Strong cliques and equistability of EPT graphs
Alcón, Liliana Graciela
Ept Graph
Equistable Graph
General Partition Graph
Strong Clique
Triangle Condition
Triangle Graph
title_short Strong cliques and equistability of EPT graphs
title_full Strong cliques and equistability of EPT graphs
title_fullStr Strong cliques and equistability of EPT graphs
title_full_unstemmed Strong cliques and equistability of EPT graphs
title_sort Strong cliques and equistability of EPT graphs
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Gutierrez, Marisa
Kovács, István
Milanič, Martin
Rizzi, Romeo
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutierrez, Marisa
Kovács, István
Milanič, Martin
Rizzi, Romeo
author_role author
author2 Gutierrez, Marisa
Kovács, István
Milanič, Martin
Rizzi, Romeo
author2_role author
author
author
author
dc.subject.none.fl_str_mv Ept Graph
Equistable Graph
General Partition Graph
Strong Clique
Triangle Condition
Triangle Graph
topic Ept Graph
Equistable Graph
General Partition Graph
Strong Clique
Triangle Condition
Triangle Graph
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we characterize the equistable graphs within the class of EPT graphs, the edge-intersection graphs of paths in a tree. This result generalizes a previously known characterization of equistable line graphs. Our approach is based on the combinatorial features of triangle graphs and general partition graphs. We also show that, in EPT graphs, testing whether a given clique is strong is co-NP-complete. We obtain this hardness result by first showing hardness of the problem of determining whether a given graph has a maximal matching disjoint from a given edge cut. As a positive result, we prove that the problem of testing whether a given clique is strong is polynomial in the class of local EPT graphs, which are defined as the edge intersection graphs of paths in a star and are known to coincide with the line graphs of multigraphs.
Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Kovács, István. University of Primorska; Eslovenia
Fil: Milanič, Martin. University of Primorska; Eslovenia
Fil: Rizzi, Romeo. Universita di Verona; Italia
description In this paper, we characterize the equistable graphs within the class of EPT graphs, the edge-intersection graphs of paths in a tree. This result generalizes a previously known characterization of equistable line graphs. Our approach is based on the combinatorial features of triangle graphs and general partition graphs. We also show that, in EPT graphs, testing whether a given clique is strong is co-NP-complete. We obtain this hardness result by first showing hardness of the problem of determining whether a given graph has a maximal matching disjoint from a given edge cut. As a positive result, we prove that the problem of testing whether a given clique is strong is polynomial in the class of local EPT graphs, which are defined as the edge intersection graphs of paths in a star and are known to coincide with the line graphs of multigraphs.
publishDate 2016
dc.date.none.fl_str_mv 2016-04
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/11336/54193
Alcón, Liliana Graciela; Gutierrez, Marisa; Kovács, István; Milanič, Martin; Rizzi, Romeo; Strong cliques and equistability of EPT graphs; Elsevier Science; Discrete Applied Mathematics; 203; 4-2016; 13-25
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/54193
identifier_str_mv Alcón, Liliana Graciela; Gutierrez, Marisa; Kovács, István; Milanič, Martin; Rizzi, Romeo; Strong cliques and equistability of EPT graphs; Elsevier Science; Discrete Applied Mathematics; 203; 4-2016; 13-25
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/url/https://www.sciencedirect.com/science/article/pii/S0166218X15004771
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2015.09.016
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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score 13.069144

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