Let k ∈ N and let G be a graph. A function f : V(G) → 2~([k]) is a rainbow function if, for every vertex x with f(x) = Ø, f(N(x)) = [k], where [k] denotes the integers ranging from 1 to k. The rainbow domination number γ_(kr)(G) is the minimum of ∑_(x∈V(G))|f(x)| over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs.
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