Dichotomies properties on computational complexity of S-packing coloring problems

الأصل · EN

This work establishes the complexity class of several instances of the S-packing coloring problem: for a graph G, a positive integer k and a non decreasing list of integers S = (s_1,..., s_k), G is S-colorable, if its vertices can be partitioned into sets S_i, i = 1,..., k, where each S_i being a s_i -packing (a set of vertices at pairwise distance greater than s_i). For a list of three integers, a dichotomy between NP-complete problems and polynomial time solvable problems is determined for subcubic graphs. Moreover, for an unfixed size of list, the complexity of the S-packing coloring problem is determined for several instances of the problem. These properties are used in order to prove a dichotomy between NP-complete problems and polynomial time solvable problems for lists of at most four integers.