Before revision:  Appl. Math. 2012 .  As a byproduct, we get that deciding whether V(G) can be partitioned into 3 subsets each inducing a complete bipartite graph is NP-complete.
After revision:  Appl. Math. 2012 . , we present ours as an alternative simpler one. As a byproduct, we get that deciding whether V(G) can be partitioned into 3 subsets each inducing a complete bipartite graph is NP-complete.