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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/260361
Ver los metadatos del registro completo
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oai:ri.conicet.gov.ar:11336/260361 |
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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 Técnicas2025-09-29T10:03:17Zoai: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:34982025-09-29 10:03:18.068CONICET 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 |
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13.070432 |