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

Zelinka, Bohdan

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