Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs

Autores
Argiroffo, Gabriela Rut; Leoni, Valeria Alejandra; Torres, Pablo Daniel
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider two variations of graph total domination, namely, k-tuple total domination and total {k}-domination (for a fixed positive integer k). Their related decision problems are both NP-complete even for bipartite graphs. In this work, we study some subclasses of bipartite graphs. We prove the NP-completeness of both problems (for every fixed k) for bipartite planar graphs and we provide an APX-hardness result for the total domination problem for bipartite subcubic graphs. In addition, we introduce a more general variation of total domination (total (r,m)-domination) that allows us to design a specific linear time algorithm for bipartite distance-hereditary graphs. In particular, it returns a minimum weight total {k}-dominating function for bipartite distance-hereditary graphs.
Fil: Argiroffo, Gabriela Rut. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Leoni, Valeria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Torres, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ciencias Básicas; Argentina
Materia
BIPARTITE GRAPH
COMPUTATIONAL COMPLEXITY
K-TUPLE TOTAL DOMINATION
TOTAL {K}-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:11336/100784
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphsArgiroffo, Gabriela RutLeoni, Valeria AlejandraTorres, Pablo DanielBIPARTITE GRAPHCOMPUTATIONAL COMPLEXITYK-TUPLE TOTAL DOMINATIONTOTAL {K}-DOMINATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider two variations of graph total domination, namely, k-tuple total domination and total {k}-domination (for a fixed positive integer k). Their related decision problems are both NP-complete even for bipartite graphs. In this work, we study some subclasses of bipartite graphs. We prove the NP-completeness of both problems (for every fixed k) for bipartite planar graphs and we provide an APX-hardness result for the total domination problem for bipartite subcubic graphs. In addition, we introduce a more general variation of total domination (total (r,m)-domination) that allows us to design a specific linear time algorithm for bipartite distance-hereditary graphs. In particular, it returns a minimum weight total {k}-dominating function for bipartite distance-hereditary graphs.Fil: Argiroffo, Gabriela Rut. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Leoni, Valeria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Torres, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ciencias Básicas; ArgentinaElsevier Science2018-10info: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/11336/100784Argiroffo, Gabriela Rut; Leoni, Valeria Alejandra; Torres, Pablo Daniel; Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs; Elsevier Science; Information Processing Letters; 138; 10-2018; 75-800020-0190CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0020019018301327info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ipl.2018.06.007info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:36:45Zoai:ri.conicet.gov.ar:11336/100784instacron: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 09:36:46.106CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs
title Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs
spellingShingle Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs
Argiroffo, Gabriela Rut
BIPARTITE GRAPH
COMPUTATIONAL COMPLEXITY
K-TUPLE TOTAL DOMINATION
TOTAL {K}-DOMINATION
title_short Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs
title_full Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs
title_fullStr Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs
title_full_unstemmed Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs
title_sort Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs
dc.creator.none.fl_str_mv Argiroffo, Gabriela Rut
Leoni, Valeria Alejandra
Torres, Pablo Daniel
author Argiroffo, Gabriela Rut
author_facet Argiroffo, Gabriela Rut
Leoni, Valeria Alejandra
Torres, Pablo Daniel
author_role author
author2 Leoni, Valeria Alejandra
Torres, Pablo Daniel
author2_role author
author
dc.subject.none.fl_str_mv BIPARTITE GRAPH
COMPUTATIONAL COMPLEXITY
K-TUPLE TOTAL DOMINATION
TOTAL {K}-DOMINATION
topic BIPARTITE GRAPH
COMPUTATIONAL COMPLEXITY
K-TUPLE TOTAL DOMINATION
TOTAL {K}-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 We consider two variations of graph total domination, namely, k-tuple total domination and total {k}-domination (for a fixed positive integer k). Their related decision problems are both NP-complete even for bipartite graphs. In this work, we study some subclasses of bipartite graphs. We prove the NP-completeness of both problems (for every fixed k) for bipartite planar graphs and we provide an APX-hardness result for the total domination problem for bipartite subcubic graphs. In addition, we introduce a more general variation of total domination (total (r,m)-domination) that allows us to design a specific linear time algorithm for bipartite distance-hereditary graphs. In particular, it returns a minimum weight total {k}-dominating function for bipartite distance-hereditary graphs.
Fil: Argiroffo, Gabriela Rut. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Leoni, Valeria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Torres, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Escuela de Ciencias Básicas; Argentina
description We consider two variations of graph total domination, namely, k-tuple total domination and total {k}-domination (for a fixed positive integer k). Their related decision problems are both NP-complete even for bipartite graphs. In this work, we study some subclasses of bipartite graphs. We prove the NP-completeness of both problems (for every fixed k) for bipartite planar graphs and we provide an APX-hardness result for the total domination problem for bipartite subcubic graphs. In addition, we introduce a more general variation of total domination (total (r,m)-domination) that allows us to design a specific linear time algorithm for bipartite distance-hereditary graphs. In particular, it returns a minimum weight total {k}-dominating function for bipartite distance-hereditary graphs.
publishDate 2018
dc.date.none.fl_str_mv 2018-10
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/11336/100784
Argiroffo, Gabriela Rut; Leoni, Valeria Alejandra; Torres, Pablo Daniel; Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs; Elsevier Science; Information Processing Letters; 138; 10-2018; 75-80
0020-0190
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100784
identifier_str_mv Argiroffo, Gabriela Rut; Leoni, Valeria Alejandra; Torres, Pablo Daniel; Complexity of k-tuple total and total {k}-dominations for some subclasses of bipartite graphs; Elsevier Science; Information Processing Letters; 138; 10-2018; 75-80
0020-0190
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/abs/pii/S0020019018301327
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ipl.2018.06.007
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
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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