Abstract
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) = ∅, 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 Σ x∈V(G) |f(x)| over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs.