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...
| Authors: | , , |
|---|---|
| Format: | article |
| Status: | Published version |
| Publication Date: | 2011 |
| Country: | Argentina |
| Institution: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repository: | Biblioteca Digital (UBA-FCEN) |
| Language: | English |
| OAI Identifier: | paperaa:paper_0166218X_v159_n1_p60_Velasquez |
| Online Access: | http://hdl.handle.net/20.500.12110/paper_0166218X_v159_n1_p60_Velasquez |
| Access Level: | Open access |
| Keyword: | 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 |
| Summary: | 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. |
|---|