k-tuple colorings of the Cartesian product of graphs

Autores
Bonomo, Flavia; Koch, Ivo Valerio; Torres, Pablo; Valencia Pabon, Mario
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χk(G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(G□H)=max{χ(G),χ(H)}. In this paper, we show that there exist graphs G and H such that χk(G□H)>max{χk(G),χk(H)} for k≥2. Moreover, we also show that there exist graph families such that, for any k≥1, the k-tuple chromatic number of their Cartesian product is equal to the maximum k-tuple chromatic number of its factors.
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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento. Instituto de Industria; Argentina
Fil: Torres, Pablo. 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: Valencia Pabon, Mario. Universite de Paris 13-Nord; Francia. Centre National de la Recherche Scientifique; Francia
Materia
CARTESIAN PRODUCT OF GRAPHS
CAYLEY GRAPHS
HOM-IDEMPOTENT GRAPHS
K-TUPLE COLORINGS
KNESER 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:11336/97048
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling k-tuple colorings of the Cartesian product of graphsBonomo, FlaviaKoch, Ivo ValerioTorres, PabloValencia Pabon, MarioCARTESIAN PRODUCT OF GRAPHSCAYLEY GRAPHSHOM-IDEMPOTENT GRAPHSK-TUPLE COLORINGSKNESER GRAPHShttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χk(G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(G□H)=max{χ(G),χ(H)}. In this paper, we show that there exist graphs G and H such that χk(G□H)>max{χk(G),χk(H)} for k≥2. Moreover, we also show that there exist graph families such that, for any k≥1, the k-tuple chromatic number of their Cartesian product is equal to the maximum k-tuple chromatic number of its factors.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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento. Instituto de Industria; ArgentinaFil: Torres, Pablo. 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: Valencia Pabon, Mario. Universite de Paris 13-Nord; Francia. Centre National de la Recherche Scientifique; FranciaElsevier Science2017-01info: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/11336/97048Bonomo, Flavia; Koch, Ivo Valerio; Torres, Pablo; Valencia Pabon, Mario; k-tuple colorings of the Cartesian product of graphs; Elsevier Science; Discrete Applied Mathematics; 245; 1-2017; 177-1820166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2017.02.003info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X17300872info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:22:24Zoai:ri.conicet.gov.ar:11336/97048instacron: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:34982025-10-15 15:22:24.503CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv k-tuple colorings of the Cartesian product of graphs
title k-tuple colorings of the Cartesian product of graphs
spellingShingle k-tuple colorings of the Cartesian product of graphs
Bonomo, Flavia
CARTESIAN PRODUCT OF GRAPHS
CAYLEY GRAPHS
HOM-IDEMPOTENT GRAPHS
K-TUPLE COLORINGS
KNESER GRAPHS
title_short k-tuple colorings of the Cartesian product of graphs
title_full k-tuple colorings of the Cartesian product of graphs
title_fullStr k-tuple colorings of the Cartesian product of graphs
title_full_unstemmed k-tuple colorings of the Cartesian product of graphs
title_sort k-tuple colorings of the Cartesian product of graphs
dc.creator.none.fl_str_mv Bonomo, Flavia
Koch, Ivo Valerio
Torres, Pablo
Valencia Pabon, Mario
author Bonomo, Flavia
author_facet Bonomo, Flavia
Koch, Ivo Valerio
Torres, Pablo
Valencia Pabon, Mario
author_role author
author2 Koch, Ivo Valerio
Torres, Pablo
Valencia Pabon, Mario
author2_role author
author
author
dc.subject.none.fl_str_mv CARTESIAN PRODUCT OF GRAPHS
CAYLEY GRAPHS
HOM-IDEMPOTENT GRAPHS
K-TUPLE COLORINGS
KNESER GRAPHS
topic CARTESIAN PRODUCT OF GRAPHS
CAYLEY GRAPHS
HOM-IDEMPOTENT GRAPHS
K-TUPLE COLORINGS
KNESER GRAPHS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χk(G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(G□H)=max{χ(G),χ(H)}. In this paper, we show that there exist graphs G and H such that χk(G□H)>max{χk(G),χk(H)} for k≥2. Moreover, we also show that there exist graph families such that, for any k≥1, the k-tuple chromatic number of their Cartesian product is equal to the maximum k-tuple chromatic number of its factors.
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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento. Instituto de Industria; Argentina
Fil: Torres, Pablo. 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: Valencia Pabon, Mario. Universite de Paris 13-Nord; Francia. Centre National de la Recherche Scientifique; Francia
description A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χk(G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(G□H)=max{χ(G),χ(H)}. In this paper, we show that there exist graphs G and H such that χk(G□H)>max{χk(G),χk(H)} for k≥2. Moreover, we also show that there exist graph families such that, for any k≥1, the k-tuple chromatic number of their Cartesian product is equal to the maximum k-tuple chromatic number of its factors.
publishDate 2017
dc.date.none.fl_str_mv 2017-01
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/11336/97048
Bonomo, Flavia; Koch, Ivo Valerio; Torres, Pablo; Valencia Pabon, Mario; k-tuple colorings of the Cartesian product of graphs; Elsevier Science; Discrete Applied Mathematics; 245; 1-2017; 177-182
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/97048
identifier_str_mv Bonomo, Flavia; Koch, Ivo Valerio; Torres, Pablo; Valencia Pabon, Mario; k-tuple colorings of the Cartesian product of graphs; Elsevier Science; Discrete Applied Mathematics; 245; 1-2017; 177-182
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.2017.02.003
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X17300872
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 13.22299

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