On coloring problems with local constraints

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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, t...

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Detalles Bibliográficos
Autores principales:	Bonomo, F., Faenza, Y., Oriolo, G.
Formato:	JOUR
Materias:	Clique-trees Computational complexity Graph coloring Unit interval graphs
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0012365X_v312_n12-13_p2027_Bonomo
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_0012365X_v312_n12-13_p2027_Bonomo2023-10-03T14:10:22Z On coloring problems with local constraints Bonomo, F. Faenza, Y. Oriolo, G. Clique-trees Computational complexity Graph coloring Unit interval graphs 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. Durn, J. Marenco, Exploring the complexity boundary between coloring and list-coloring, Annals of Operations Research 169 (1) (2009) 3-16]. © 2012 Elsevier B.V. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0012365X_v312_n12-13_p2027_Bonomo
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Clique-trees Computational complexity Graph coloring Unit interval graphs
spellingShingle	Clique-trees Computational complexity Graph coloring Unit interval graphs Bonomo, F. Faenza, Y. Oriolo, G. On coloring problems with local constraints
topic_facet	Clique-trees Computational complexity Graph coloring Unit interval graphs
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. Durn, J. Marenco, Exploring the complexity boundary between coloring and list-coloring, Annals of Operations Research 169 (1) (2009) 3-16]. © 2012 Elsevier B.V. All rights reserved.
format	JOUR
author	Bonomo, F. Faenza, Y. Oriolo, G.
author_facet	Bonomo, F. Faenza, Y. Oriolo, G.
author_sort	Bonomo, F.
title	On coloring problems with local constraints
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
url	http://hdl.handle.net/20.500.12110/paper_0012365X_v312_n12-13_p2027_Bonomo
work_keys_str_mv	AT bonomof oncoloringproblemswithlocalconstraints AT faenzay oncoloringproblemswithlocalconstraints AT oriolog oncoloringproblemswithlocalconstraints
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On coloring problems with local constraints

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