## Domatic numbers of graphs and their variants: A survey.(English)Zbl 0894.05026

Haynes, Teresa W. (ed.) et al., Domination in graphs. Advanced topics. New York, NY: Marcel Dekker. Pure Appl. Math., Marcel Dekker. 209, 351-377 (1998).
The domatic number $$d(G)$$ of a graph $$G$$ is the maximum number of classes in a partition of the vertex set of $$G$$ such that each class is a dominating set in $$G$$. It is thus a domination-analogue to the chromatic number, which asks for partitions into independent sets. This paper gives a survey of results on the domatic number and its numerous variants, among them the total domatic number, the adomatic, idomatic, $$k$$-domatic, edge-domatic, complementarily domatic, semidomatic and antidomatic numbers.
For the entire collection see [Zbl 0883.00011].
Reviewer: P.Braß (Berlin)

### MSC:

 05C35 Extremal problems in graph theory

### Keywords:

domination; domatic number