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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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