Graphs whose vertices of degree at least 2 lie in a triangle

Autores
do Forte, Vinicius L.; Lin, Min Chih; Lucena, Abilio; Maculan, Nelson; Moyano, Verónica Andrea; Szwarcfiter, Jayme L.
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A pendant vertex is one of degree one and an isolated vertex has degree zero. A neighborhood star-free (NSF for short) graph is one in which every vertex is contained in a triangle except pendant vertices and isolated vertices. This class has been considered before for several contexts. In the present paper, we study the complexity of the dominating induced matching (DIM) problem and the perfect edge domination (PED) problem for NSF graphs. We prove the corresponding decision problems are NP-Complete for several of its subclasses. As an added value of this study, we show three connected variants of planar positive 1in3SAT are also NP-Complete. Since these variants are more basic in complexity theory context than many graph problems, these results can be useful to prove that other problems are NP-Complete.
Fil: do Forte, Vinicius L.. Universidade Federal Rural do Rio de Janeiro; Brasil
Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lucena, Abilio. Universidade Federal do Rio de Janeiro; Brasil
Fil: Maculan, Nelson. Universidade Federal do Rio de Janeiro; Brasil
Fil: Moyano, Verónica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil
Materia
NEIGHBORHOOD STAR-FREE GRAPHS
TRIANGLE
EFFICIENT EDGE DOMINATION
PERFECT EDGE DOMINATION
DOMINATING INDUCED MATCHING
CONNECTED PLANAR POSITIVE 1in3SAT
CONNECTED CUBIC PLANAR POSITIVE 1in3SAT
CONNECTED SUBCUBIC PLANAR C4-FREE POSITIVE 1in3SAT
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/260361
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Graphs whose vertices of degree at least 2 lie in a triangledo Forte, Vinicius L.Lin, Min ChihLucena, AbilioMaculan, NelsonMoyano, Verónica AndreaSzwarcfiter, Jayme L.NEIGHBORHOOD STAR-FREE GRAPHSTRIANGLEEFFICIENT EDGE DOMINATIONPERFECT EDGE DOMINATIONDOMINATING INDUCED MATCHINGCONNECTED PLANAR POSITIVE 1in3SATCONNECTED CUBIC PLANAR POSITIVE 1in3SATCONNECTED SUBCUBIC PLANAR C4-FREE POSITIVE 1in3SAThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A pendant vertex is one of degree one and an isolated vertex has degree zero. A neighborhood star-free (NSF for short) graph is one in which every vertex is contained in a triangle except pendant vertices and isolated vertices. This class has been considered before for several contexts. In the present paper, we study the complexity of the dominating induced matching (DIM) problem and the perfect edge domination (PED) problem for NSF graphs. We prove the corresponding decision problems are NP-Complete for several of its subclasses. As an added value of this study, we show three connected variants of planar positive 1in3SAT are also NP-Complete. Since these variants are more basic in complexity theory context than many graph problems, these results can be useful to prove that other problems are NP-Complete.Fil: do Forte, Vinicius L.. Universidade Federal Rural do Rio de Janeiro; BrasilFil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lucena, Abilio. Universidade Federal do Rio de Janeiro; BrasilFil: Maculan, Nelson. Universidade Federal do Rio de Janeiro; BrasilFil: Moyano, Verónica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; BrasilEDP Sciences2024-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/260361do Forte, Vinicius L.; Lin, Min Chih; Lucena, Abilio; Maculan, Nelson; Moyano, Verónica Andrea; et al.; Graphs whose vertices of degree at least 2 lie in a triangle; EDP Sciences; Rairo - Recherche Operationnelle (operations Research); 58; 6; 12-2024; 5063-50770399-0559CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1051/ro/2024198info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:33:05Zoai:ri.conicet.gov.ar:11336/260361instacron: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:34982025-10-22 11:33:05.266CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Graphs whose vertices of degree at least 2 lie in a triangle
title Graphs whose vertices of degree at least 2 lie in a triangle
spellingShingle Graphs whose vertices of degree at least 2 lie in a triangle
do Forte, Vinicius L.
NEIGHBORHOOD STAR-FREE GRAPHS
TRIANGLE
EFFICIENT EDGE DOMINATION
PERFECT EDGE DOMINATION
DOMINATING INDUCED MATCHING
CONNECTED PLANAR POSITIVE 1in3SAT
CONNECTED CUBIC PLANAR POSITIVE 1in3SAT
CONNECTED SUBCUBIC PLANAR C4-FREE POSITIVE 1in3SAT
title_short Graphs whose vertices of degree at least 2 lie in a triangle
title_full Graphs whose vertices of degree at least 2 lie in a triangle
title_fullStr Graphs whose vertices of degree at least 2 lie in a triangle
title_full_unstemmed Graphs whose vertices of degree at least 2 lie in a triangle
title_sort Graphs whose vertices of degree at least 2 lie in a triangle
dc.creator.none.fl_str_mv do Forte, Vinicius L.
Lin, Min Chih
Lucena, Abilio
Maculan, Nelson
Moyano, Verónica Andrea
Szwarcfiter, Jayme L.
author do Forte, Vinicius L.
author_facet do Forte, Vinicius L.
Lin, Min Chih
Lucena, Abilio
Maculan, Nelson
Moyano, Verónica Andrea
Szwarcfiter, Jayme L.
author_role author
author2 Lin, Min Chih
Lucena, Abilio
Maculan, Nelson
Moyano, Verónica Andrea
Szwarcfiter, Jayme L.
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv NEIGHBORHOOD STAR-FREE GRAPHS
TRIANGLE
EFFICIENT EDGE DOMINATION
PERFECT EDGE DOMINATION
DOMINATING INDUCED MATCHING
CONNECTED PLANAR POSITIVE 1in3SAT
CONNECTED CUBIC PLANAR POSITIVE 1in3SAT
CONNECTED SUBCUBIC PLANAR C4-FREE POSITIVE 1in3SAT
topic NEIGHBORHOOD STAR-FREE GRAPHS
TRIANGLE
EFFICIENT EDGE DOMINATION
PERFECT EDGE DOMINATION
DOMINATING INDUCED MATCHING
CONNECTED PLANAR POSITIVE 1in3SAT
CONNECTED CUBIC PLANAR POSITIVE 1in3SAT
CONNECTED SUBCUBIC PLANAR C4-FREE POSITIVE 1in3SAT
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A pendant vertex is one of degree one and an isolated vertex has degree zero. A neighborhood star-free (NSF for short) graph is one in which every vertex is contained in a triangle except pendant vertices and isolated vertices. This class has been considered before for several contexts. In the present paper, we study the complexity of the dominating induced matching (DIM) problem and the perfect edge domination (PED) problem for NSF graphs. We prove the corresponding decision problems are NP-Complete for several of its subclasses. As an added value of this study, we show three connected variants of planar positive 1in3SAT are also NP-Complete. Since these variants are more basic in complexity theory context than many graph problems, these results can be useful to prove that other problems are NP-Complete.
Fil: do Forte, Vinicius L.. Universidade Federal Rural do Rio de Janeiro; Brasil
Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lucena, Abilio. Universidade Federal do Rio de Janeiro; Brasil
Fil: Maculan, Nelson. Universidade Federal do Rio de Janeiro; Brasil
Fil: Moyano, Verónica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil
description A pendant vertex is one of degree one and an isolated vertex has degree zero. A neighborhood star-free (NSF for short) graph is one in which every vertex is contained in a triangle except pendant vertices and isolated vertices. This class has been considered before for several contexts. In the present paper, we study the complexity of the dominating induced matching (DIM) problem and the perfect edge domination (PED) problem for NSF graphs. We prove the corresponding decision problems are NP-Complete for several of its subclasses. As an added value of this study, we show three connected variants of planar positive 1in3SAT are also NP-Complete. Since these variants are more basic in complexity theory context than many graph problems, these results can be useful to prove that other problems are NP-Complete.
publishDate 2024
dc.date.none.fl_str_mv 2024-12
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/11336/260361
do Forte, Vinicius L.; Lin, Min Chih; Lucena, Abilio; Maculan, Nelson; Moyano, Verónica Andrea; et al.; Graphs whose vertices of degree at least 2 lie in a triangle; EDP Sciences; Rairo - Recherche Operationnelle (operations Research); 58; 6; 12-2024; 5063-5077
0399-0559
CONICET Digital
CONICET
url http://hdl.handle.net/11336/260361
identifier_str_mv do Forte, Vinicius L.; Lin, Min Chih; Lucena, Abilio; Maculan, Nelson; Moyano, Verónica Andrea; et al.; Graphs whose vertices of degree at least 2 lie in a triangle; EDP Sciences; Rairo - Recherche Operationnelle (operations Research); 58; 6; 12-2024; 5063-5077
0399-0559
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1051/ro/2024198
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv EDP Sciences
publisher.none.fl_str_mv EDP Sciences
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
_version_ 1846781943914430464
score 12.982451

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