On the b-coloring of P4-tidy graphs

• Autores: Velasquez, C.I.B.; Bonomo, F.; Koch, I.
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Discrete Appl Math 2011;159(1):60-68
• Materia: 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
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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.