The B-Domatic Number of a Graph

@inproceedings{Favaron2013TheBN,
  title={The B-Domatic Number of a Graph},
  author={Odile Favaron},
  booktitle={Discuss. Math. Graph Theory},
  year={2013}
}
  • O. Favaron
  • Published in Discuss. Math. Graph Theory 1 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… 
2 Citations

On the b-Domatic Number of Graphs

TLDR
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.

Some new results on the b-domatic number of graphs

TLDR
It is proved that for any graph G on n vertices, bd ( G )+ bd( Ġ ) ≤ n +1, where Ġ  is the complement of G.

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TLDR
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