On dominating set polyhedra of circular interval graphs

Autores
Bianchi, Silvia María; Nasini, Graciela Leonor; Tolomei, Paola Beatriz; Torres, Luis Miguel
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Clique-node and closed neighborhood matrices of circular interval graphs are circular matrices. The stable set polytope and the dominating set polytope on these graphs are therefore closely related to the set packing polytope and the set covering polyhedron on circular matrices. Eisenbrand et al. [18] take advantage of this relationship to propose a complete linear description of the stable set polytope on circular interval graphs. In this paper we follow similar ideas to obtain a complete description of the dominating set polytope on the same class of graphs. As in the packing case, our results are established for a larger class of covering polyhedra of the form Q ∗ (A, b) := conv {x ∈ Z n + : Ax ≥ b}, with A a circular matrix and b an integer vector. These results also provide linear descriptions of polyhedra associated with several variants of the dominating set problem on circular interval graphs.
Fil: Bianchi, Silvia María. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Tolomei, Paola Beatriz. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Torres, Luis Miguel. Escuela Politécnica Nacional; Ecuador
Materia
CIRCULANT MINOR
CIRCULAR MATRIX
COVERING POLYHEDRA
DOMINATING SETS
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:11336/153322
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On dominating set polyhedra of circular interval graphsBianchi, Silvia MaríaNasini, Graciela LeonorTolomei, Paola BeatrizTorres, Luis MiguelCIRCULANT MINORCIRCULAR MATRIXCOVERING POLYHEDRADOMINATING SETShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Clique-node and closed neighborhood matrices of circular interval graphs are circular matrices. The stable set polytope and the dominating set polytope on these graphs are therefore closely related to the set packing polytope and the set covering polyhedron on circular matrices. Eisenbrand et al. [18] take advantage of this relationship to propose a complete linear description of the stable set polytope on circular interval graphs. In this paper we follow similar ideas to obtain a complete description of the dominating set polytope on the same class of graphs. As in the packing case, our results are established for a larger class of covering polyhedra of the form Q ∗ (A, b) := conv {x ∈ Z n + : Ax ≥ b}, with A a circular matrix and b an integer vector. These results also provide linear descriptions of polyhedra associated with several variants of the dominating set problem on circular interval graphs.Fil: Bianchi, Silvia María. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Tolomei, Paola Beatriz. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Torres, Luis Miguel. Escuela Politécnica Nacional; EcuadorElsevier Science2021-04info: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/11336/153322Bianchi, Silvia María; Nasini, Graciela Leonor; Tolomei, Paola Beatriz; Torres, Luis Miguel; On dominating set polyhedra of circular interval graphs; Elsevier Science; Discrete Mathematics; 344; 4; 4-2021; 1-250012-365X1872-681XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0012365X20304696info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2020.112283info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1712.07057info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:53:56Zoai:ri.conicet.gov.ar:11336/153322instacron: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:34982025-11-05 10:53:56.776CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On dominating set polyhedra of circular interval graphs
title On dominating set polyhedra of circular interval graphs
spellingShingle On dominating set polyhedra of circular interval graphs
Bianchi, Silvia María
CIRCULANT MINOR
CIRCULAR MATRIX
COVERING POLYHEDRA
DOMINATING SETS
title_short On dominating set polyhedra of circular interval graphs
title_full On dominating set polyhedra of circular interval graphs
title_fullStr On dominating set polyhedra of circular interval graphs
title_full_unstemmed On dominating set polyhedra of circular interval graphs
title_sort On dominating set polyhedra of circular interval graphs
dc.creator.none.fl_str_mv Bianchi, Silvia María
Nasini, Graciela Leonor
Tolomei, Paola Beatriz
Torres, Luis Miguel
author Bianchi, Silvia María
author_facet Bianchi, Silvia María
Nasini, Graciela Leonor
Tolomei, Paola Beatriz
Torres, Luis Miguel
author_role author
author2 Nasini, Graciela Leonor
Tolomei, Paola Beatriz
Torres, Luis Miguel
author2_role author
author
author
dc.subject.none.fl_str_mv CIRCULANT MINOR
CIRCULAR MATRIX
COVERING POLYHEDRA
DOMINATING SETS
topic CIRCULANT MINOR
CIRCULAR MATRIX
COVERING POLYHEDRA
DOMINATING SETS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Clique-node and closed neighborhood matrices of circular interval graphs are circular matrices. The stable set polytope and the dominating set polytope on these graphs are therefore closely related to the set packing polytope and the set covering polyhedron on circular matrices. Eisenbrand et al. [18] take advantage of this relationship to propose a complete linear description of the stable set polytope on circular interval graphs. In this paper we follow similar ideas to obtain a complete description of the dominating set polytope on the same class of graphs. As in the packing case, our results are established for a larger class of covering polyhedra of the form Q ∗ (A, b) := conv {x ∈ Z n + : Ax ≥ b}, with A a circular matrix and b an integer vector. These results also provide linear descriptions of polyhedra associated with several variants of the dominating set problem on circular interval graphs.
Fil: Bianchi, Silvia María. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Tolomei, Paola Beatriz. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Torres, Luis Miguel. Escuela Politécnica Nacional; Ecuador
description Clique-node and closed neighborhood matrices of circular interval graphs are circular matrices. The stable set polytope and the dominating set polytope on these graphs are therefore closely related to the set packing polytope and the set covering polyhedron on circular matrices. Eisenbrand et al. [18] take advantage of this relationship to propose a complete linear description of the stable set polytope on circular interval graphs. In this paper we follow similar ideas to obtain a complete description of the dominating set polytope on the same class of graphs. As in the packing case, our results are established for a larger class of covering polyhedra of the form Q ∗ (A, b) := conv {x ∈ Z n + : Ax ≥ b}, with A a circular matrix and b an integer vector. These results also provide linear descriptions of polyhedra associated with several variants of the dominating set problem on circular interval graphs.
publishDate 2021
dc.date.none.fl_str_mv 2021-04
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/11336/153322
Bianchi, Silvia María; Nasini, Graciela Leonor; Tolomei, Paola Beatriz; Torres, Luis Miguel; On dominating set polyhedra of circular interval graphs; Elsevier Science; Discrete Mathematics; 344; 4; 4-2021; 1-25
0012-365X
1872-681X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/153322
identifier_str_mv Bianchi, Silvia María; Nasini, Graciela Leonor; Tolomei, Paola Beatriz; Torres, Luis Miguel; On dominating set polyhedra of circular interval graphs; Elsevier Science; Discrete Mathematics; 344; 4; 4-2021; 1-25
0012-365X
1872-681X
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/S0012365X20304696
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2020.112283
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1712.07057
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
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 13.084122

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