On a heterochromatic number for hypercubes

The neighbourhood heterochromatic numbernh"c(G) of a non-empty graph G is the smallest integer l such that for every colouring of G with exactly l colours, G contains a vertex all of whose neighbours have different colours. We prove that lim"n"->"~(nh"c(G^n)-1)/|V(G^n)|=1 for any connected graph G with at least two vertices. We also give upper and lower bounds for the neighbourhood heterochromatic number of the 2^n-dimensional hypercube.