On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size

Autores
Lin, Min Chih; Mizrahi, Michel Jonathan
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the computational complexity of the minimum dominating set problem on graphs restricted by forbidden induced subgraphs. We give some dichotomies results for the problem on graphs defined by any combination of forbidden induced subgraphs with at most four vertices, implying either an NP-Hardness proof or a polynomial time algorithm. We also extend the results by showing that dominating set problem remains NP-hard even when the graph has maximum degree three, it is planar and has no induced claw, induced diamond, induced K4 nor induced cycle of length 4, 5, 7, 8, 9, 10 and 11.
Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Mizrahi, Michel Jonathan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Algorithms
Complexity
Dominating Set
Forbidden Induced Subgraphs
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:11336/59587
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59587
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small sizeLin, Min ChihMizrahi, Michel JonathanAlgorithmsComplexityDominating SetForbidden Induced Subgraphshttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We study the computational complexity of the minimum dominating set problem on graphs restricted by forbidden induced subgraphs. We give some dichotomies results for the problem on graphs defined by any combination of forbidden induced subgraphs with at most four vertices, implying either an NP-Hardness proof or a polynomial time algorithm. We also extend the results by showing that dominating set problem remains NP-hard even when the graph has maximum degree three, it is planar and has no induced claw, induced diamond, induced K4 nor induced cycle of length 4, 5, 7, 8, 9, 10 and 11.Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mizrahi, Michel Jonathan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2015-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/59587Lin, Min Chih; Mizrahi, Michel Jonathan; On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size; Elsevier Science; Discrete Applied Mathematics; 197; 12-2015; 53-580166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2015.02.010info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X15000967info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:40:41Zoai:ri.conicet.gov.ar:11336/59587instacron: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 10:40:41.463CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size
title On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size
spellingShingle On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size
Lin, Min Chih
Algorithms
Complexity
Dominating Set
Forbidden Induced Subgraphs
title_short On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size
title_full On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size
title_fullStr On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size
title_full_unstemmed On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size
title_sort On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size
dc.creator.none.fl_str_mv Lin, Min Chih
Mizrahi, Michel Jonathan
author Lin, Min Chih
author_facet Lin, Min Chih
Mizrahi, Michel Jonathan
author_role author
author2 Mizrahi, Michel Jonathan
author2_role author
dc.subject.none.fl_str_mv Algorithms
Complexity
Dominating Set
Forbidden Induced Subgraphs
topic Algorithms
Complexity
Dominating Set
Forbidden Induced Subgraphs
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the computational complexity of the minimum dominating set problem on graphs restricted by forbidden induced subgraphs. We give some dichotomies results for the problem on graphs defined by any combination of forbidden induced subgraphs with at most four vertices, implying either an NP-Hardness proof or a polynomial time algorithm. We also extend the results by showing that dominating set problem remains NP-hard even when the graph has maximum degree three, it is planar and has no induced claw, induced diamond, induced K4 nor induced cycle of length 4, 5, 7, 8, 9, 10 and 11.
Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Mizrahi, Michel Jonathan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We study the computational complexity of the minimum dominating set problem on graphs restricted by forbidden induced subgraphs. We give some dichotomies results for the problem on graphs defined by any combination of forbidden induced subgraphs with at most four vertices, implying either an NP-Hardness proof or a polynomial time algorithm. We also extend the results by showing that dominating set problem remains NP-hard even when the graph has maximum degree three, it is planar and has no induced claw, induced diamond, induced K4 nor induced cycle of length 4, 5, 7, 8, 9, 10 and 11.
publishDate 2015
dc.date.none.fl_str_mv 2015-12
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/11336/59587
Lin, Min Chih; Mizrahi, Michel Jonathan; On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size; Elsevier Science; Discrete Applied Mathematics; 197; 12-2015; 53-58
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59587
identifier_str_mv Lin, Min Chih; Mizrahi, Michel Jonathan; On the complexity of the minimum domination problem restricted by forbidden induced subgraphs of small size; Elsevier Science; Discrete Applied Mathematics; 197; 12-2015; 53-58
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/doi/10.1016/j.dam.2015.02.010
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X15000967
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
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
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score 13.070432

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