@inproceedings{Favaron2013TheBN,
title={The B-Domatic Number of a Graph},
author={Odile Favaron},
booktitle={Discuss. Math. Graph Theory},
year={2013}
}

Published in Discuss. Math. Graph Theory1 September 2013

Mathematics

Abstract Besides the classical chromatic and achromatic numbers of a graph related to minimum or minimal vertex partitions into independent sets, the b-chromatic number was introduced in 1998 thanks to an alternative definition of the minimality of such partitions. When independent sets are replaced by dominating sets, the parameters corresponding to the chromatic and achromatic numbers are the domatic and adomatic numbers d(G) and ad(G). We introduce the b-domatic number bd(G) as the… Expand

Some properties of b-Domatic partitions are explained, the minimum cardinality of a b-domatic partition of G is called the b- domatic number and is denoted by bd(G), and some families of graphs are determined.Expand

The b-chromatic number b(G) of a graph G = (V, E) is the largest integer k such that G admits a vertex partition into k independent sets Xi (i = 1, . . . , k) such that each Xi contains a vertex xi… Expand

Four general upper bounds on the b-chromatic number χb(G) are established and it is proved that special graphs with disconnected graphs and graphs with independence number 2 are b-continuous.Expand