The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs

Autores
Dobson, Maria Patricia; Leoni, Valeria Alejandra; Nasini, Graciela Leonor
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The notion of k-limited packing in a graph is a generalization of 2-packing. For a given non negative integer k, a subset B of vertices is a k-limited packing if there are at most k elements of B in the closed neighborhood of every vertex. On the other side, a k-tuple domination set in a graph is a subset of vertices D such that every vertex has at least k elements of D in its closed neighborhood. In this work we first reveal a strong relationship between these notions, and obtain from a result due to Liao and Chang (2002), the polynomiality of the k-limited packing problem for strongly chordal graphs.We also prove that, in coincidence with the case of domination, the k-limited packing problem is NP-complete for split graphs. Finally, we prove that both problems are polynomial for the non-perfect class of P4-tidy graphs, including the perfect classes of P4-sparse graphs and cographs.
Fil: Dobson, Maria Patricia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Leoni, Valeria Alejandra. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Nasini, Graciela Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
COMPUTATIONAL COMPLEXITY
K-LIMITED PACKING
K-TUPLE DOMINATING SET
P4-TIDY GRAPHS
SPLIT GRAPHS
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:11336/100300
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphsDobson, Maria PatriciaLeoni, Valeria AlejandraNasini, Graciela LeonorCOMPUTATIONAL COMPLEXITYK-LIMITED PACKINGK-TUPLE DOMINATING SETP4-TIDY GRAPHSSPLIT GRAPHShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The notion of k-limited packing in a graph is a generalization of 2-packing. For a given non negative integer k, a subset B of vertices is a k-limited packing if there are at most k elements of B in the closed neighborhood of every vertex. On the other side, a k-tuple domination set in a graph is a subset of vertices D such that every vertex has at least k elements of D in its closed neighborhood. In this work we first reveal a strong relationship between these notions, and obtain from a result due to Liao and Chang (2002), the polynomiality of the k-limited packing problem for strongly chordal graphs.We also prove that, in coincidence with the case of domination, the k-limited packing problem is NP-complete for split graphs. Finally, we prove that both problems are polynomial for the non-perfect class of P4-tidy graphs, including the perfect classes of P4-sparse graphs and cographs.Fil: Dobson, Maria Patricia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Leoni, Valeria Alejandra. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Nasini, Graciela Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaElsevier Science2010-08info: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/11336/100300Dobson, Maria Patricia; Leoni, Valeria Alejandra; Nasini, Graciela Leonor; The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs; Elsevier Science; Electronic Notes in Discrete Mathematics; 36; C; 8-2010; 559-5661571-0653CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.endm.2010.05.071info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S1571065310000727info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:36:17Zoai:ri.conicet.gov.ar:11336/100300instacron: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 09:36:17.933CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs
title The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs
spellingShingle The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs
Dobson, Maria Patricia
COMPUTATIONAL COMPLEXITY
K-LIMITED PACKING
K-TUPLE DOMINATING SET
P4-TIDY GRAPHS
SPLIT GRAPHS
title_short The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs
title_full The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs
title_fullStr The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs
title_full_unstemmed The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs
title_sort The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs
dc.creator.none.fl_str_mv Dobson, Maria Patricia
Leoni, Valeria Alejandra
Nasini, Graciela Leonor
author Dobson, Maria Patricia
author_facet Dobson, Maria Patricia
Leoni, Valeria Alejandra
Nasini, Graciela Leonor
author_role author
author2 Leoni, Valeria Alejandra
Nasini, Graciela Leonor
author2_role author
author
dc.subject.none.fl_str_mv COMPUTATIONAL COMPLEXITY
K-LIMITED PACKING
K-TUPLE DOMINATING SET
P4-TIDY GRAPHS
SPLIT GRAPHS
topic COMPUTATIONAL COMPLEXITY
K-LIMITED PACKING
K-TUPLE DOMINATING SET
P4-TIDY GRAPHS
SPLIT GRAPHS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The notion of k-limited packing in a graph is a generalization of 2-packing. For a given non negative integer k, a subset B of vertices is a k-limited packing if there are at most k elements of B in the closed neighborhood of every vertex. On the other side, a k-tuple domination set in a graph is a subset of vertices D such that every vertex has at least k elements of D in its closed neighborhood. In this work we first reveal a strong relationship between these notions, and obtain from a result due to Liao and Chang (2002), the polynomiality of the k-limited packing problem for strongly chordal graphs.We also prove that, in coincidence with the case of domination, the k-limited packing problem is NP-complete for split graphs. Finally, we prove that both problems are polynomial for the non-perfect class of P4-tidy graphs, including the perfect classes of P4-sparse graphs and cographs.
Fil: Dobson, Maria Patricia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Leoni, Valeria Alejandra. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Nasini, Graciela Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description The notion of k-limited packing in a graph is a generalization of 2-packing. For a given non negative integer k, a subset B of vertices is a k-limited packing if there are at most k elements of B in the closed neighborhood of every vertex. On the other side, a k-tuple domination set in a graph is a subset of vertices D such that every vertex has at least k elements of D in its closed neighborhood. In this work we first reveal a strong relationship between these notions, and obtain from a result due to Liao and Chang (2002), the polynomiality of the k-limited packing problem for strongly chordal graphs.We also prove that, in coincidence with the case of domination, the k-limited packing problem is NP-complete for split graphs. Finally, we prove that both problems are polynomial for the non-perfect class of P4-tidy graphs, including the perfect classes of P4-sparse graphs and cographs.
publishDate 2010
dc.date.none.fl_str_mv 2010-08
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/11336/100300
Dobson, Maria Patricia; Leoni, Valeria Alejandra; Nasini, Graciela Leonor; The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs; Elsevier Science; Electronic Notes in Discrete Mathematics; 36; C; 8-2010; 559-566
1571-0653
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100300
identifier_str_mv Dobson, Maria Patricia; Leoni, Valeria Alejandra; Nasini, Graciela Leonor; The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs; Elsevier Science; Electronic Notes in Discrete Mathematics; 36; C; 8-2010; 559-566
1571-0653
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.endm.2010.05.071
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S1571065310000727
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
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score 13.070432

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