On coloring problems with local constraints

Autores
Bonomo, Flavia; Faenza, Yuri; Oriolo, Gianpaolo
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We deal with some generalizations of the graph coloring problem on classes of perfect graphs. Namely we consider the μ-coloring problem (upper bounds for the color on each vertex), the precoloring extension problem (a subset of vertices colored beforehand), and a problem generalizing both of them, the (γ,μ)-coloring problem (lower and upper bounds for the color on each vertex). We characterize the complexity of all those problems on clique-trees of different heights, providing polynomial-time algorithms for the cases that are easy. These results have interesting corollaries. First, one can observe on clique-trees of different heights the increasing complexity of the chain k-coloring, μ-coloring, (γ,μ)-coloring, and list-coloring. Second, clique-trees of height 2 are the first known example of a class of graphs where μ-coloring is polynomial-time solvable and precoloring extension is NP-complete, thus being at the same time the first example where μ-coloring is polynomially solvable and (γ,μ)-coloring is NP-complete. Last, we show that theμ-coloring problem on unit interval graphs is NP-complete. These results answer three questions from Bonomo et al. [F. Bonomo, G. Durán, J. Marenco, Exploring the complexity boundary between coloring and list-coloring, Annals of Operations Research 169 (1) (2009) 3–16].
Fil: Bonomo, Flavia. Universita Tor Vergata; Italia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Fil: Faenza, Yuri. Universita Di Padova; Italia
Fil: Oriolo, Gianpaolo. Universita Tor Vergata; Italia
Materia
Graph Coloring
Clique-Trees
Unit Interval Graphs
Computational Complexity
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:11336/14888
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14888
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On coloring problems with local constraintsBonomo, FlaviaFaenza, YuriOriolo, GianpaoloGraph ColoringClique-TreesUnit Interval GraphsComputational Complexityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We deal with some generalizations of the graph coloring problem on classes of perfect graphs. Namely we consider the μ-coloring problem (upper bounds for the color on each vertex), the precoloring extension problem (a subset of vertices colored beforehand), and a problem generalizing both of them, the (γ,μ)-coloring problem (lower and upper bounds for the color on each vertex). We characterize the complexity of all those problems on clique-trees of different heights, providing polynomial-time algorithms for the cases that are easy. These results have interesting corollaries. First, one can observe on clique-trees of different heights the increasing complexity of the chain k-coloring, μ-coloring, (γ,μ)-coloring, and list-coloring. Second, clique-trees of height 2 are the first known example of a class of graphs where μ-coloring is polynomial-time solvable and precoloring extension is NP-complete, thus being at the same time the first example where μ-coloring is polynomially solvable and (γ,μ)-coloring is NP-complete. Last, we show that theμ-coloring problem on unit interval graphs is NP-complete. These results answer three questions from Bonomo et al. [F. Bonomo, G. Durán, J. Marenco, Exploring the complexity boundary between coloring and list-coloring, Annals of Operations Research 169 (1) (2009) 3–16].Fil: Bonomo, Flavia. Universita Tor Vergata; Italia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Faenza, Yuri. Universita Di Padova; ItaliaFil: Oriolo, Gianpaolo. Universita Tor Vergata; ItaliaElsevier2012-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14888Bonomo, Flavia; Faenza, Yuri; Oriolo, Gianpaolo; On coloring problems with local constraints; Elsevier; Discrete Mathematics; 312; 12-13; 4-2012; 2027-20390012-365Xenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2012.03.019info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0012365X12001343info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:55:28Zoai:ri.conicet.gov.ar:11336/14888instacron: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 09:55:28.692CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On coloring problems with local constraints
title On coloring problems with local constraints
spellingShingle On coloring problems with local constraints
Bonomo, Flavia
Graph Coloring
Clique-Trees
Unit Interval Graphs
Computational Complexity
title_short On coloring problems with local constraints
title_full On coloring problems with local constraints
title_fullStr On coloring problems with local constraints
title_full_unstemmed On coloring problems with local constraints
title_sort On coloring problems with local constraints
dc.creator.none.fl_str_mv Bonomo, Flavia
Faenza, Yuri
Oriolo, Gianpaolo
author Bonomo, Flavia
author_facet Bonomo, Flavia
Faenza, Yuri
Oriolo, Gianpaolo
author_role author
author2 Faenza, Yuri
Oriolo, Gianpaolo
author2_role author
author
dc.subject.none.fl_str_mv Graph Coloring
Clique-Trees
Unit Interval Graphs
Computational Complexity
topic Graph Coloring
Clique-Trees
Unit Interval Graphs
Computational Complexity
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 We deal with some generalizations of the graph coloring problem on classes of perfect graphs. Namely we consider the μ-coloring problem (upper bounds for the color on each vertex), the precoloring extension problem (a subset of vertices colored beforehand), and a problem generalizing both of them, the (γ,μ)-coloring problem (lower and upper bounds for the color on each vertex). We characterize the complexity of all those problems on clique-trees of different heights, providing polynomial-time algorithms for the cases that are easy. These results have interesting corollaries. First, one can observe on clique-trees of different heights the increasing complexity of the chain k-coloring, μ-coloring, (γ,μ)-coloring, and list-coloring. Second, clique-trees of height 2 are the first known example of a class of graphs where μ-coloring is polynomial-time solvable and precoloring extension is NP-complete, thus being at the same time the first example where μ-coloring is polynomially solvable and (γ,μ)-coloring is NP-complete. Last, we show that theμ-coloring problem on unit interval graphs is NP-complete. These results answer three questions from Bonomo et al. [F. Bonomo, G. Durán, J. Marenco, Exploring the complexity boundary between coloring and list-coloring, Annals of Operations Research 169 (1) (2009) 3–16].
Fil: Bonomo, Flavia. Universita Tor Vergata; Italia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Fil: Faenza, Yuri. Universita Di Padova; Italia
Fil: Oriolo, Gianpaolo. Universita Tor Vergata; Italia
description We deal with some generalizations of the graph coloring problem on classes of perfect graphs. Namely we consider the μ-coloring problem (upper bounds for the color on each vertex), the precoloring extension problem (a subset of vertices colored beforehand), and a problem generalizing both of them, the (γ,μ)-coloring problem (lower and upper bounds for the color on each vertex). We characterize the complexity of all those problems on clique-trees of different heights, providing polynomial-time algorithms for the cases that are easy. These results have interesting corollaries. First, one can observe on clique-trees of different heights the increasing complexity of the chain k-coloring, μ-coloring, (γ,μ)-coloring, and list-coloring. Second, clique-trees of height 2 are the first known example of a class of graphs where μ-coloring is polynomial-time solvable and precoloring extension is NP-complete, thus being at the same time the first example where μ-coloring is polynomially solvable and (γ,μ)-coloring is NP-complete. Last, we show that theμ-coloring problem on unit interval graphs is NP-complete. These results answer three questions from Bonomo et al. [F. Bonomo, G. Durán, J. Marenco, Exploring the complexity boundary between coloring and list-coloring, Annals of Operations Research 169 (1) (2009) 3–16].
publishDate 2012
dc.date.none.fl_str_mv 2012-04
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/11336/14888
Bonomo, Flavia; Faenza, Yuri; Oriolo, Gianpaolo; On coloring problems with local constraints; Elsevier; Discrete Mathematics; 312; 12-13; 4-2012; 2027-2039
0012-365X
url http://hdl.handle.net/11336/14888
identifier_str_mv Bonomo, Flavia; Faenza, Yuri; Oriolo, Gianpaolo; On coloring problems with local constraints; Elsevier; Discrete Mathematics; 312; 12-13; 4-2012; 2027-2039
0012-365X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2012.03.019
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0012365X12001343
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
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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