For a pair of positive parameters D,χ, partition P the vertex set V an n-vertex graph G=(V,E) into disjoint clusters diameter at most D each is called (D,χ) network decomposition, if supergraph G(P), obtained by contracting P, can be properly χ-colored. The decomposition said to strong (resp., weak) has D, i.e., for every cluster C∈P and two vertices u,v∈C, distance between them in induced G(C)...