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]. The rainbow domination number
γkr​(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