Perfect edge domination: hard and solvable cases

Autores
Lin, Min Chih; Lozin, Vadim; Moyano, Verónica Andrea; Szwarcfiter, Jayme L.
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let G be an undirected graph. An edge of Gdominates itself and all edges adjacent to it. A subset E′ of edges of G is an edge dominating set of G, if every edge of the graph is dominated by some edge of E′. We say that E′ is a perfect edge dominating set of G, if every edge not in E′ is dominated by exactly one edge of E′. The perfect edge dominating problem is to determine a least cardinality perfect edge dominating set of G. For this problem, we describe two NP-completeness proofs, for the classes of claw-free graphs of degree at most 3, and for bounded degree graphs, of maximum degree at most d≥ 3 and large girth. In contrast, we prove that the problem admits an O(n) time solution, for cubic claw-free graphs. In addition, we prove a complexity dichotomy theorem for the perfect edge domination problem, based on the results described in the paper. Finally, we describe a linear time algorithm for finding a minimum weight perfect edge dominating set of a P5-free graph. The algorithm is robust, in the sense that, given an arbitrary graph G, either it computes a minimum weight perfect edge dominating set of G, or it exhibits an induced subgraph of G, isomorphic to a P5.
Fil: Lin, Min Chih. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Lozin, Vadim. University of Warwick; Reino Unido
Fil: Moyano, Verónica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil. Instituto Nacional de Metrologia, Qualidade e Tecnologia; Brasil
Materia
CLAW-FREE GRAPHS
COMPLEXITY DICHOTOMY
CUBIC GRAPHS
NP-COMPLETENESS
PERFECT EDGE DOMINATION
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:11336/60143
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Perfect edge domination: hard and solvable casesLin, Min ChihLozin, VadimMoyano, Verónica AndreaSzwarcfiter, Jayme L.CLAW-FREE GRAPHSCOMPLEXITY DICHOTOMYCUBIC GRAPHSNP-COMPLETENESSPERFECT EDGE DOMINATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let G be an undirected graph. An edge of Gdominates itself and all edges adjacent to it. A subset E′ of edges of G is an edge dominating set of G, if every edge of the graph is dominated by some edge of E′. We say that E′ is a perfect edge dominating set of G, if every edge not in E′ is dominated by exactly one edge of E′. The perfect edge dominating problem is to determine a least cardinality perfect edge dominating set of G. For this problem, we describe two NP-completeness proofs, for the classes of claw-free graphs of degree at most 3, and for bounded degree graphs, of maximum degree at most d≥ 3 and large girth. In contrast, we prove that the problem admits an O(n) time solution, for cubic claw-free graphs. In addition, we prove a complexity dichotomy theorem for the perfect edge domination problem, based on the results described in the paper. Finally, we describe a linear time algorithm for finding a minimum weight perfect edge dominating set of a P5-free graph. The algorithm is robust, in the sense that, given an arbitrary graph G, either it computes a minimum weight perfect edge dominating set of G, or it exhibits an induced subgraph of G, isomorphic to a P5.Fil: Lin, Min Chih. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Lozin, Vadim. University of Warwick; Reino UnidoFil: Moyano, Verónica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil. Instituto Nacional de Metrologia, Qualidade e Tecnologia; BrasilSpringer2018-05info: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/11336/60143Lin, Min Chih; Lozin, Vadim; Moyano, Verónica Andrea; Szwarcfiter, Jayme L.; Perfect edge domination: hard and solvable cases; Springer; Annals Of Operations Research; 264; 1-2; 5-2018; 287-3050254-53301572-9338CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10479-017-2664-3info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10479-017-2664-3info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1705.08379info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:46:13Zoai:ri.conicet.gov.ar:11336/60143instacron: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 10:46:13.424CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Perfect edge domination: hard and solvable cases
title Perfect edge domination: hard and solvable cases
spellingShingle Perfect edge domination: hard and solvable cases
Lin, Min Chih
CLAW-FREE GRAPHS
COMPLEXITY DICHOTOMY
CUBIC GRAPHS
NP-COMPLETENESS
PERFECT EDGE DOMINATION
title_short Perfect edge domination: hard and solvable cases
title_full Perfect edge domination: hard and solvable cases
title_fullStr Perfect edge domination: hard and solvable cases
title_full_unstemmed Perfect edge domination: hard and solvable cases
title_sort Perfect edge domination: hard and solvable cases
dc.creator.none.fl_str_mv Lin, Min Chih
Lozin, Vadim
Moyano, Verónica Andrea
Szwarcfiter, Jayme L.
author Lin, Min Chih
author_facet Lin, Min Chih
Lozin, Vadim
Moyano, Verónica Andrea
Szwarcfiter, Jayme L.
author_role author
author2 Lozin, Vadim
Moyano, Verónica Andrea
Szwarcfiter, Jayme L.
author2_role author
author
author
dc.subject.none.fl_str_mv CLAW-FREE GRAPHS
COMPLEXITY DICHOTOMY
CUBIC GRAPHS
NP-COMPLETENESS
PERFECT EDGE DOMINATION
topic CLAW-FREE GRAPHS
COMPLEXITY DICHOTOMY
CUBIC GRAPHS
NP-COMPLETENESS
PERFECT EDGE DOMINATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let G be an undirected graph. An edge of Gdominates itself and all edges adjacent to it. A subset E′ of edges of G is an edge dominating set of G, if every edge of the graph is dominated by some edge of E′. We say that E′ is a perfect edge dominating set of G, if every edge not in E′ is dominated by exactly one edge of E′. The perfect edge dominating problem is to determine a least cardinality perfect edge dominating set of G. For this problem, we describe two NP-completeness proofs, for the classes of claw-free graphs of degree at most 3, and for bounded degree graphs, of maximum degree at most d≥ 3 and large girth. In contrast, we prove that the problem admits an O(n) time solution, for cubic claw-free graphs. In addition, we prove a complexity dichotomy theorem for the perfect edge domination problem, based on the results described in the paper. Finally, we describe a linear time algorithm for finding a minimum weight perfect edge dominating set of a P5-free graph. The algorithm is robust, in the sense that, given an arbitrary graph G, either it computes a minimum weight perfect edge dominating set of G, or it exhibits an induced subgraph of G, isomorphic to a P5.
Fil: Lin, Min Chih. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Lozin, Vadim. University of Warwick; Reino Unido
Fil: Moyano, Verónica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil. Instituto Nacional de Metrologia, Qualidade e Tecnologia; Brasil
description Let G be an undirected graph. An edge of Gdominates itself and all edges adjacent to it. A subset E′ of edges of G is an edge dominating set of G, if every edge of the graph is dominated by some edge of E′. We say that E′ is a perfect edge dominating set of G, if every edge not in E′ is dominated by exactly one edge of E′. The perfect edge dominating problem is to determine a least cardinality perfect edge dominating set of G. For this problem, we describe two NP-completeness proofs, for the classes of claw-free graphs of degree at most 3, and for bounded degree graphs, of maximum degree at most d≥ 3 and large girth. In contrast, we prove that the problem admits an O(n) time solution, for cubic claw-free graphs. In addition, we prove a complexity dichotomy theorem for the perfect edge domination problem, based on the results described in the paper. Finally, we describe a linear time algorithm for finding a minimum weight perfect edge dominating set of a P5-free graph. The algorithm is robust, in the sense that, given an arbitrary graph G, either it computes a minimum weight perfect edge dominating set of G, or it exhibits an induced subgraph of G, isomorphic to a P5.
publishDate 2018
dc.date.none.fl_str_mv 2018-05
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/11336/60143
Lin, Min Chih; Lozin, Vadim; Moyano, Verónica Andrea; Szwarcfiter, Jayme L.; Perfect edge domination: hard and solvable cases; Springer; Annals Of Operations Research; 264; 1-2; 5-2018; 287-305
0254-5330
1572-9338
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60143
identifier_str_mv Lin, Min Chih; Lozin, Vadim; Moyano, Verónica Andrea; Szwarcfiter, Jayme L.; Perfect edge domination: hard and solvable cases; Springer; Annals Of Operations Research; 264; 1-2; 5-2018; 287-305
0254-5330
1572-9338
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10479-017-2664-3
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10479-017-2664-3
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1705.08379
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
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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score 13.070432

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