Dichotomies properties on computational complexity of S-packing coloring problems

Nicolas Gastineau (1)

1 Equipe Combinatoire

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.

Mots clés: d-distance coloring; NP-hard problem; distance; Packing chromatic number; S-packing chromatic number; d-distance coloring.

Domaines: Informatique [cs]; Mathématique discrète [cs.DM]; Informatique [cs]; Complexité [cs.CC]

Nicolas Gastineau. Dichotomies properties on computational complexity of S-packing coloring problems. Discrete Mathematics, 2015, 338, pp.1029-1041. ⟨hal-00920502v3⟩