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Assume we have a set of k colors and to each vertex of a graph G we assign an arbitrary subset of these colors. If we require that each vertex to which an empty set is assigned has in its neighborhood all k colors, then this is called the k-rainbow dominating function of a graph G. The corresponding invariant γ rk (G), which is the minimum sum of numbers of assigned colors over all vertices of G, is called the k-rainbow domination number of G. In this paper we connect this new concept to usualdoi:10.11650/twjm/1500602498 fatcat:arkaotf2aras5fmvtlpf4lyocq