Some bounds for the \(b\)-chromatic number of a graph
type: Item
instance of: scholarly article
title: Some bounds for the \(b\)-chromatic number of a graph
zbMATH Open document ID: 1008.05056
DOI: 10.1016/S0012-365X(01)00469-1
author: Mekkia Kouider
author: Maryvonne Mahéo
published in: Discrete Mathematics
publication date: 2002-12-02T00:00:00Z
review text: The \(b\)-chromatic number of a graph \(G\) is the maximum number \(k\) of colours that can be used to colour the vertices of \(G\), such that we obtain a proper colouring of \(G\) and each colour \(i\) has at least one representant \(x_i\) adjacent to a vertex with each colour \(j\), \(1\leq j\leq k\), \(j\neq i\). Some general properties of the \(b\)-chromatic number are established. The main result provides a lower bound for the \(b\)-chromatic number of the Cartesian product of two graphs.
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1838925
zbMATH Keywords: \(b\)-colouring
zbMATH Keywords: Cartesian product
zbMATH Keywords: generalized colouring
reviewed by: Gabriel Semanišin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1838925