Kouider, Mekkia; Mahéo, Maryvonne Some bounds for the \(b\)-chromatic number of a graph. (English) Zbl 1008.05056 Discrete Math. 256, No. 1-2, 267-277 (2002). 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. Reviewer: Gabriel Semanišin (Košice) Cited in 2 ReviewsCited in 47 Documents MSC: 05C15 Coloring of graphs and hypergraphs Keywords:\(b\)-colouring; Cartesian product; generalized colouring PDFBibTeX XMLCite \textit{M. Kouider} and \textit{M. Mahéo}, Discrete Math. 256, No. 1--2, 267--277 (2002; Zbl 1008.05056) Full Text: DOI