Strong cliques and equistability of EPT graphs

Autores
Alcón, Liliana Graciela; Gutiérrez, 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.
Facultad de Ciencias Exactas
Consejo Nacional de Investigaciones Científicas y Técnicas
Materia
Matemática
Ept graph
Equistable graph
General partition graph
Strong clique
Triangle condition
Triangle graph
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/95926

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spelling Strong cliques and equistability of EPT graphsAlcón, Liliana GracielaGutiérrez, MarisaKovács, IstvánMilanič, MartinRizzi, RomeoMatemáticaEpt graphEquistable graphGeneral partition graphStrong cliqueTriangle conditionTriangle graphIn 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.Facultad de Ciencias ExactasConsejo Nacional de Investigaciones Científicas y Técnicas2016-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf13-25http://sedici.unlp.edu.ar/handle/10915/95926enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/54193info:eu-repo/semantics/altIdentifier/issn/0166-218Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2015.09.016info:eu-repo/semantics/altIdentifier/hdl/11336/54193info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-15T11:12:05Zoai:sedici.unlp.edu.ar:10915/95926Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:12:05.506SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Matemática
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
Gutiérrez, Marisa
Kovács, István
Milanič, Martin
Rizzi, Romeo
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutiérrez, Marisa
Kovács, István
Milanič, Martin
Rizzi, Romeo
author_role author
author2 Gutiérrez, Marisa
Kovács, István
Milanič, Martin
Rizzi, Romeo
author2_role author
author
author
author
dc.subject.none.fl_str_mv Matemática
Ept graph
Equistable graph
General partition graph
Strong clique
Triangle condition
Triangle graph
topic Matemática
Ept graph
Equistable graph
General partition graph
Strong clique
Triangle condition
Triangle graph
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.
Facultad de Ciencias Exactas
Consejo Nacional de Investigaciones Científicas y Técnicas
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
Articulo
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://sedici.unlp.edu.ar/handle/10915/95926
url http://sedici.unlp.edu.ar/handle/10915/95926
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/54193
info:eu-repo/semantics/altIdentifier/issn/0166-218X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2015.09.016
info:eu-repo/semantics/altIdentifier/hdl/11336/54193
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
13-25
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
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reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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