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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/95926
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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 |
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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 |
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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) |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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application/pdf 13-25 |
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SEDICI (UNLP) - Universidad Nacional de La Plata |
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