Dichotomies properties on computational complexity of SS-packing coloring problems

This work establishes the complexity class of several instances of the SS-packing coloring problem: for a graph GG, a positive integer kk and a nondecreasing list of integers S=(s1,…,sk)S=(s1,…,sk), GG is SS-colorable   if its vertices can be partitioned into sets SiSi, i=1,…,ki=1,…,k, where each SiSi is an sisi-packing (a set of vertices at pairwise distance greater than sisi). In particular we prove a dichotomy between NP-complete problems and polynomial-time solvable problems for lists of at most four integers.