On the (k,i)-coloring of cacti and complete graphs

Autores
Bonomo, Flavia; Durán, Guillermo Enrique; Koch, Ivo Valerio; Valencia Pabon, Mario
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the (k,i)-coloring problem, we aim to assign sets of colors of size k to the vertices of a graph G, so that the sets which belong to adjacent vertices of G intersect in no more than i elements and the total number of colors used is minimum. This minimum number of colors is called the (k,i)-chromatic number. We present in this work a very simple linear time algorithm to compute an optimum (k,i)- coloring of cycles and we generalize the result in order to derive a polynomial time algorithm for this problem on cacti. We also perform a slight modification to the algorithm in order to obtain a simpler algorithm for the close coloring problem addressed in [R.C. Brigham and R.D. Dutton, Generalized k-tuple colorings of cycles and other graphs, J. Combin. Theory B 32:90–94, 1982]. Finally, we present a relation between the (k,i)-coloring problem on complete graphs and weighted binary codes.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Durán, Guillermo Enrique. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento; Argentina
Fil: Valencia Pabon, Mario. Universite de Paris 13-Nord. Laboratoire d'informatique de L'Université Paris-Nord; Francia
Materia
Generalized k-tuple coloring
(k,i)-coloring
cactus
complete graphs
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:11336/103273
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/103273
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the (k,i)-coloring of cacti and complete graphsBonomo, FlaviaDurán, Guillermo EnriqueKoch, Ivo ValerioValencia Pabon, MarioGeneralized k-tuple coloring(k,i)-coloringcactuscomplete graphshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1In the (k,i)-coloring problem, we aim to assign sets of colors of size k to the vertices of a graph G, so that the sets which belong to adjacent vertices of G intersect in no more than i elements and the total number of colors used is minimum. This minimum number of colors is called the (k,i)-chromatic number. We present in this work a very simple linear time algorithm to compute an optimum (k,i)- coloring of cycles and we generalize the result in order to derive a polynomial time algorithm for this problem on cacti. We also perform a slight modification to the algorithm in order to obtain a simpler algorithm for the close coloring problem addressed in [R.C. Brigham and R.D. Dutton, Generalized k-tuple colorings of cycles and other graphs, J. Combin. Theory B 32:90–94, 1982]. Finally, we present a relation between the (k,i)-coloring problem on complete graphs and weighted binary codes.Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Durán, Guillermo Enrique. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento; ArgentinaFil: Valencia Pabon, Mario. Universite de Paris 13-Nord. Laboratoire d'informatique de L'Université Paris-Nord; FranciaCharles Babbage Res Ctr2018-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/103273Bonomo, Flavia; Durán, Guillermo Enrique; Koch, Ivo Valerio; Valencia Pabon, Mario; On the (k,i)-coloring of cacti and complete graphs; Charles Babbage Res Ctr; Ars Combinatoria; 137; 1-2018; 317-3330381-7032CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.combinatorialmath.ca/ArsCombinatoria/Vol137.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:42:54Zoai:ri.conicet.gov.ar:11336/103273instacron: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 14:42:54.565CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the (k,i)-coloring of cacti and complete graphs
title On the (k,i)-coloring of cacti and complete graphs
spellingShingle On the (k,i)-coloring of cacti and complete graphs
Bonomo, Flavia
Generalized k-tuple coloring
(k,i)-coloring
cactus
complete graphs
title_short On the (k,i)-coloring of cacti and complete graphs
title_full On the (k,i)-coloring of cacti and complete graphs
title_fullStr On the (k,i)-coloring of cacti and complete graphs
title_full_unstemmed On the (k,i)-coloring of cacti and complete graphs
title_sort On the (k,i)-coloring of cacti and complete graphs
dc.creator.none.fl_str_mv Bonomo, Flavia
Durán, Guillermo Enrique
Koch, Ivo Valerio
Valencia Pabon, Mario
author Bonomo, Flavia
author_facet Bonomo, Flavia
Durán, Guillermo Enrique
Koch, Ivo Valerio
Valencia Pabon, Mario
author_role author
author2 Durán, Guillermo Enrique
Koch, Ivo Valerio
Valencia Pabon, Mario
author2_role author
author
author
dc.subject.none.fl_str_mv Generalized k-tuple coloring
(k,i)-coloring
cactus
complete graphs
topic Generalized k-tuple coloring
(k,i)-coloring
cactus
complete graphs
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the (k,i)-coloring problem, we aim to assign sets of colors of size k to the vertices of a graph G, so that the sets which belong to adjacent vertices of G intersect in no more than i elements and the total number of colors used is minimum. This minimum number of colors is called the (k,i)-chromatic number. We present in this work a very simple linear time algorithm to compute an optimum (k,i)- coloring of cycles and we generalize the result in order to derive a polynomial time algorithm for this problem on cacti. We also perform a slight modification to the algorithm in order to obtain a simpler algorithm for the close coloring problem addressed in [R.C. Brigham and R.D. Dutton, Generalized k-tuple colorings of cycles and other graphs, J. Combin. Theory B 32:90–94, 1982]. Finally, we present a relation between the (k,i)-coloring problem on complete graphs and weighted binary codes.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Durán, Guillermo Enrique. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento; Argentina
Fil: Valencia Pabon, Mario. Universite de Paris 13-Nord. Laboratoire d'informatique de L'Université Paris-Nord; Francia
description In the (k,i)-coloring problem, we aim to assign sets of colors of size k to the vertices of a graph G, so that the sets which belong to adjacent vertices of G intersect in no more than i elements and the total number of colors used is minimum. This minimum number of colors is called the (k,i)-chromatic number. We present in this work a very simple linear time algorithm to compute an optimum (k,i)- coloring of cycles and we generalize the result in order to derive a polynomial time algorithm for this problem on cacti. We also perform a slight modification to the algorithm in order to obtain a simpler algorithm for the close coloring problem addressed in [R.C. Brigham and R.D. Dutton, Generalized k-tuple colorings of cycles and other graphs, J. Combin. Theory B 32:90–94, 1982]. Finally, we present a relation between the (k,i)-coloring problem on complete graphs and weighted binary codes.
publishDate 2018
dc.date.none.fl_str_mv 2018-01
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/11336/103273
Bonomo, Flavia; Durán, Guillermo Enrique; Koch, Ivo Valerio; Valencia Pabon, Mario; On the (k,i)-coloring of cacti and complete graphs; Charles Babbage Res Ctr; Ars Combinatoria; 137; 1-2018; 317-333
0381-7032
CONICET Digital
CONICET
url http://hdl.handle.net/11336/103273
identifier_str_mv Bonomo, Flavia; Durán, Guillermo Enrique; Koch, Ivo Valerio; Valencia Pabon, Mario; On the (k,i)-coloring of cacti and complete graphs; Charles Babbage Res Ctr; Ars Combinatoria; 137; 1-2018; 317-333
0381-7032
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.combinatorialmath.ca/ArsCombinatoria/Vol137.html
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
dc.publisher.none.fl_str_mv Charles Babbage Res Ctr
publisher.none.fl_str_mv Charles Babbage Res Ctr
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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