Domination parameters with number 2: Interrelations and algorithmic consequences

Autores
Bonomo, Flavia; Brešar, Boštjan; Grippo, Luciano Norberto; Milanič, Martin; Safe, Martin Dario
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination number, γw2(G), the 2-domination number, γ2(G), the {2}-domination number, γ{2}(G), the double domination number, γ×2(G), the total {2}-domination number, γt{2}(G), and the total double domination number, γt×2(G), where G is a graph in which the corresponding invariant is well defined. The third criterion yields rainbow versions of the mentioned six parameters, one of which has already been well studied, and three other give new interesting parameters. Together with a special, extensively studied Roman domination, γR(G), and two classical parameters, the domination number, γ(G), and the total domination number, γt(G), we consider 13 domination invariants in graphs. In the main result of the paper we present sharp upper and lower bounds of each of the invariants in terms of every other invariant, a large majority of which are new results proven in this paper. As a consequence of the main theorem we obtain new complexity results regarding the existence of approximation algorithms for the studied invariants, matched with tight or almost tight inapproximability bounds, which hold even in the class of split graphs.
Fil: Bonomo, Flavia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Fil: Brešar, Boštjan. Institute of Mathematics, Physics and Mechanics; Eslovenia. University of Maribor; Eslovenia
Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Milanič, Martin. University of Primorska; Eslovenia
Fil: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Materia
2-DOMINATION
APPROXIMATION ALGORITHM
DOUBLE DOMINATION
GRAPH DOMINATION
INAPPROXIMABILITY
INTEGER DOMINATION
RAINBOW DOMINATION
SPLIT GRAPH
TOTAL DOMINATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/97057
Acceder
id CONICETDig_4ab132bf9e6c7f35445275dce7311845
oai_identifier_str oai:ri.conicet.gov.ar:11336/97057
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Domination parameters with number 2: Interrelations and algorithmic consequencesBonomo, FlaviaBrešar, BoštjanGrippo, Luciano NorbertoMilanič, MartinSafe, Martin Dario2-DOMINATIONAPPROXIMATION ALGORITHMDOUBLE DOMINATIONGRAPH DOMINATIONINAPPROXIMABILITYINTEGER DOMINATIONRAINBOW DOMINATIONSPLIT GRAPHTOTAL DOMINATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination number, γw2(G), the 2-domination number, γ2(G), the {2}-domination number, γ{2}(G), the double domination number, γ×2(G), the total {2}-domination number, γt{2}(G), and the total double domination number, γt×2(G), where G is a graph in which the corresponding invariant is well defined. The third criterion yields rainbow versions of the mentioned six parameters, one of which has already been well studied, and three other give new interesting parameters. Together with a special, extensively studied Roman domination, γR(G), and two classical parameters, the domination number, γ(G), and the total domination number, γt(G), we consider 13 domination invariants in graphs. In the main result of the paper we present sharp upper and lower bounds of each of the invariants in terms of every other invariant, a large majority of which are new results proven in this paper. As a consequence of the main theorem we obtain new complexity results regarding the existence of approximation algorithms for the studied invariants, matched with tight or almost tight inapproximability bounds, which hold even in the class of split graphs.Fil: Bonomo, Flavia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Brešar, Boštjan. Institute of Mathematics, Physics and Mechanics; Eslovenia. University of Maribor; EsloveniaFil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Milanič, Martin. University of Primorska; EsloveniaFil: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaElsevier Science2018-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/97057Bonomo, Flavia; Brešar, Boštjan; Grippo, Luciano Norberto; Milanič, Martin; Safe, Martin Dario; Domination parameters with number 2: Interrelations and algorithmic consequences; Elsevier Science; Discrete Applied Mathematics; 235; 1-2018; 23-500166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X17304031info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2017.08.017info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1511.00410info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:56:08Zoai:ri.conicet.gov.ar:11336/97057instacron: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 09:56:09.138CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Domination parameters with number 2: Interrelations and algorithmic consequences
title Domination parameters with number 2: Interrelations and algorithmic consequences
spellingShingle Domination parameters with number 2: Interrelations and algorithmic consequences
Bonomo, Flavia
2-DOMINATION
APPROXIMATION ALGORITHM
DOUBLE DOMINATION
GRAPH DOMINATION
INAPPROXIMABILITY
INTEGER DOMINATION
RAINBOW DOMINATION
SPLIT GRAPH
TOTAL DOMINATION
title_short Domination parameters with number 2: Interrelations and algorithmic consequences
title_full Domination parameters with number 2: Interrelations and algorithmic consequences
title_fullStr Domination parameters with number 2: Interrelations and algorithmic consequences
title_full_unstemmed Domination parameters with number 2: Interrelations and algorithmic consequences
title_sort Domination parameters with number 2: Interrelations and algorithmic consequences
dc.creator.none.fl_str_mv Bonomo, Flavia
Brešar, Boštjan
Grippo, Luciano Norberto
Milanič, Martin
Safe, Martin Dario
author Bonomo, Flavia
author_facet Bonomo, Flavia
Brešar, Boštjan
Grippo, Luciano Norberto
Milanič, Martin
Safe, Martin Dario
author_role author
author2 Brešar, Boštjan
Grippo, Luciano Norberto
Milanič, Martin
Safe, Martin Dario
author2_role author
author
author
author
dc.subject.none.fl_str_mv 2-DOMINATION
APPROXIMATION ALGORITHM
DOUBLE DOMINATION
GRAPH DOMINATION
INAPPROXIMABILITY
INTEGER DOMINATION
RAINBOW DOMINATION
SPLIT GRAPH
TOTAL DOMINATION
topic 2-DOMINATION
APPROXIMATION ALGORITHM
DOUBLE DOMINATION
GRAPH DOMINATION
INAPPROXIMABILITY
INTEGER DOMINATION
RAINBOW DOMINATION
SPLIT GRAPH
TOTAL 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 In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination number, γw2(G), the 2-domination number, γ2(G), the {2}-domination number, γ{2}(G), the double domination number, γ×2(G), the total {2}-domination number, γt{2}(G), and the total double domination number, γt×2(G), where G is a graph in which the corresponding invariant is well defined. The third criterion yields rainbow versions of the mentioned six parameters, one of which has already been well studied, and three other give new interesting parameters. Together with a special, extensively studied Roman domination, γR(G), and two classical parameters, the domination number, γ(G), and the total domination number, γt(G), we consider 13 domination invariants in graphs. In the main result of the paper we present sharp upper and lower bounds of each of the invariants in terms of every other invariant, a large majority of which are new results proven in this paper. As a consequence of the main theorem we obtain new complexity results regarding the existence of approximation algorithms for the studied invariants, matched with tight or almost tight inapproximability bounds, which hold even in the class of split graphs.
Fil: Bonomo, Flavia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Fil: Brešar, Boštjan. Institute of Mathematics, Physics and Mechanics; Eslovenia. University of Maribor; Eslovenia
Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Milanič, Martin. University of Primorska; Eslovenia
Fil: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
description In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination number, γw2(G), the 2-domination number, γ2(G), the {2}-domination number, γ{2}(G), the double domination number, γ×2(G), the total {2}-domination number, γt{2}(G), and the total double domination number, γt×2(G), where G is a graph in which the corresponding invariant is well defined. The third criterion yields rainbow versions of the mentioned six parameters, one of which has already been well studied, and three other give new interesting parameters. Together with a special, extensively studied Roman domination, γR(G), and two classical parameters, the domination number, γ(G), and the total domination number, γt(G), we consider 13 domination invariants in graphs. In the main result of the paper we present sharp upper and lower bounds of each of the invariants in terms of every other invariant, a large majority of which are new results proven in this paper. As a consequence of the main theorem we obtain new complexity results regarding the existence of approximation algorithms for the studied invariants, matched with tight or almost tight inapproximability bounds, which hold even in the class of split graphs.
publishDate 2018
dc.date.none.fl_str_mv 2018-01
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/11336/97057
Bonomo, Flavia; Brešar, Boštjan; Grippo, Luciano Norberto; Milanič, Martin; Safe, Martin Dario; Domination parameters with number 2: Interrelations and algorithmic consequences; Elsevier Science; Discrete Applied Mathematics; 235; 1-2018; 23-50
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/97057
identifier_str_mv Bonomo, Flavia; Brešar, Boštjan; Grippo, Luciano Norberto; Milanič, Martin; Safe, Martin Dario; Domination parameters with number 2: Interrelations and algorithmic consequences; Elsevier Science; Discrete Applied Mathematics; 235; 1-2018; 23-50
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/S0166218X17304031
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2017.08.017
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1511.00410
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
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
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_ 1842269386632593408
score 13.13397

Publicaciones similares