On the b-coloring of P4-tidy graphs

A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χb(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G i...

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Detalles Bibliográficos
Autores: Velasquez, C.I.B., Bonomo, F., Koch, I.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:Argentina
Institución:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
Repositorio:Biblioteca Digital (UBA-FCEN)
Idioma:inglés
OAI Identifier:paperaa:paper_0166218X_v159_n1_p60_Velasquez
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0166218X_v159_n1_p60_Velasquez
Access Level:acceso abierto
Palabra clave:b-coloring
b-continuity
b-monotonicity
P4-tidy graphs
B-chromatic number
Chromatic number
Graph G
Induced subgraphs
Monotonicity
Polynomial-time algorithms
Color
Coloring
Graphic methods
Polynomial approximation
Graph theory
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spelling On the b-coloring of P4-tidy graphsVelasquez, C.I.B.Bonomo, F.Koch, I.b-coloringb-continuityb-monotonicityP4-tidy graphsB-chromatic numberb-coloringb-continuityChromatic numberGraph GInduced subgraphsMonotonicityP4-tidy graphsPolynomial-time algorithmsColorColoringGraphic methodsPolynomial approximationGraph theoryA b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χb(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every t=χ(G),...,χb(G), and it is b-monotonic if χb(H1)<χb(H2) for every induced subgraph H1 of G, and every induced subgraph H2 of H1. In this work, we prove that P4-tidy graphs (a generalization of many classes of graphs with few induced P4s) are b-continuous and b-monotonic. Furthermore, we describe a polynomial time algorithm to compute theb-chromatic number for this class of graphs. © 2010 Elsevier B.V. All rights reserved.Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Koch, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0166218X_v159_n1_p60_VelasquezDiscrete Appl Math 2011;159(1):60-68reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2024-05-10T10:42:47Zpaperaa:paper_0166218X_v159_n1_p60_VelasquezInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962024-05-10 10:42:48.242Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv On the b-coloring of P4-tidy graphs
title On the b-coloring of P4-tidy graphs
spellingShingle On the b-coloring of P4-tidy graphs
Velasquez, C.I.B.
b-coloring
b-continuity
b-monotonicity
P4-tidy graphs
B-chromatic number
b-coloring
b-continuity
Chromatic number
Graph G
Induced subgraphs
Monotonicity
P4-tidy graphs
Polynomial-time algorithms
Color
Coloring
Graphic methods
Polynomial approximation
Graph theory
title_short On the b-coloring of P4-tidy graphs
title_full On the b-coloring of P4-tidy graphs
title_fullStr On the b-coloring of P4-tidy graphs
title_full_unstemmed On the b-coloring of P4-tidy graphs
title_sort On the b-coloring of P4-tidy graphs
dc.creator.none.fl_str_mv Velasquez, C.I.B.
Bonomo, F.
Koch, I.
author Velasquez, C.I.B.
author_facet Velasquez, C.I.B.
Bonomo, F.
Koch, I.
author_role author
author2 Bonomo, F.
Koch, I.
author2_role author
author
dc.subject.none.fl_str_mv b-coloring
b-continuity
b-monotonicity
P4-tidy graphs
B-chromatic number
b-coloring
b-continuity
Chromatic number
Graph G
Induced subgraphs
Monotonicity
P4-tidy graphs
Polynomial-time algorithms
Color
Coloring
Graphic methods
Polynomial approximation
Graph theory
topic b-coloring
b-continuity
b-monotonicity
P4-tidy graphs
B-chromatic number
b-coloring
b-continuity
Chromatic number
Graph G
Induced subgraphs
Monotonicity
P4-tidy graphs
Polynomial-time algorithms
Color
Coloring
Graphic methods
Polynomial approximation
Graph theory
description A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χb(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every t=χ(G),...,χb(G), and it is b-monotonic if χb(H1)<χb(H2) for every induced subgraph H1 of G, and every induced subgraph H2 of H1. In this work, we prove that P4-tidy graphs (a generalization of many classes of graphs with few induced P4s) are b-continuous and b-monotonic. Furthermore, we describe a polynomial time algorithm to compute theb-chromatic number for this class of graphs. © 2010 Elsevier B.V. All rights reserved.
publishDate 2011
dc.date.none.fl_str_mv 2011
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/20.500.12110/paper_0166218X_v159_n1_p60_Velasquez
url http://hdl.handle.net/20.500.12110/paper_0166218X_v159_n1_p60_Velasquez
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Discrete Appl Math 2011;159(1):60-68
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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