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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/54193
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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 Técnicas2025-09-03T10:00:29Zoai: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:34982025-09-03 10:00:29.368CONICET 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 |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.13397 |