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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paper:paper_0166218X_v159_n1_p60_Velasquez2023-06-08T15:15:30Z On the b-coloring of P4-tidy graphs Bonomo, Flavia Koch, Ivo 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 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. 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. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v159_n1_p60_Velasquez http://hdl.handle.net/20.500.12110/paper_0166218X_v159_n1_p60_Velasquez |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
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 |
spellingShingle |
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 Bonomo, Flavia Koch, Ivo On the b-coloring of P4-tidy graphs |
topic_facet |
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. |
author |
Bonomo, Flavia Koch, Ivo |
author_facet |
Bonomo, Flavia Koch, Ivo |
author_sort |
Bonomo, Flavia |
title |
On the b-coloring of P4-tidy graphs |
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 |
publishDate |
2011 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v159_n1_p60_Velasquez http://hdl.handle.net/20.500.12110/paper_0166218X_v159_n1_p60_Velasquez |
work_keys_str_mv |
AT bonomoflavia onthebcoloringofp4tidygraphs AT kochivo onthebcoloringofp4tidygraphs |
_version_ |
1768544546634858496 |