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On k-domatic numbers of graphs. (English) Zbl 0537.05050
A k-dominating set in the graph G is a subset D of V(G) with the property that for each vertex \(x\in V(G)-D\) there exists a vertex \(y\in D\) such that for the distance between x and y we have \(d(x,y)\leq k.\) A k-domatic partition of G is a partition of V(G) into k-dominating sets in G. The maximum number of classes of a k-domatic partition is called the k- domatic number of G and is denoted by \(d_ k(G)\). The author shows a.o. that \(d_ k(G)\geq \min(n,k+1)\) and calculates \(d_ k(C_ n)\).
Reviewer: C.Hoede

MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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References:
[1] Borowiecki M., Kuzak M.: On the \(k\)-stable and \(k\)-dominating sets of graphs. Graphs, Hypergraphs and Block Systems. Proc. Symp. Zielona Góra 1976 by M. Borowiecki, Z. Skupień, L. Szamkołowicz, Zielona Góra 1976. · Zbl 0344.05143
[2] Cockayne E. J., Hedetniemi S. T.: Towards a theory of domination in graphs. Networks 7 (1977), 247-261. · Zbl 0384.05051
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