Coloring the edges of a random graph without a monochromatic giant component

We study the following two problems: i) Given a random graph G(n,m) (a graph drawn uniformly at random from all graphs on n vertices with exactly m edges), can we color its edges with r colors such that no color class contains a component of size Theta(n)? ii) Given a random graph G(n,m) with a random partition of its edge set into sets of size r, can we color its edges with r colors subject to the restriction that every color is used for exactly one edge in every set of the partition such that no color class contains a component of size Theta(n)? We prove that for any fixed r >= 2, in both settings the (sharp) threshold for the existence of such a coloring coincides with the known threshold for r-orientability of G(n,m), which is at m = rc(r)*n for some analytically computable constant c(r)*. The fact that the two problems have the same threshold is in contrast with known results for the two corresponding Achlioptas-type problems.