%0 Journal Article %T Dichotomies properties on computational complexity of S-packing coloring problems %+ Equipe Combinatoire %A Gastineau, Nicolas %Z Financement région Bourgogne %< avec comité de lecture %@ 0012-365X %J Discrete Mathematics %I Elsevier %V 338 %P 1029–1041 %8 2015 %D 2015 %Z 1312.5280 %K d-distance coloring %K NP-hard problem %K distance %K Packing chromatic number %K S-packing chromatic number %K d-distance coloring. %Z Computer Science [cs]/Discrete Mathematics [cs.DM] %Z Computer Science [cs]/Computational Complexity [cs.CC]Journal articles %X 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. %G English %2 https://u-bourgogne.hal.science/hal-00920502v3/document %2 https://u-bourgogne.hal.science/hal-00920502v3/file/comp_S_packing_arxiv.pdf %L hal-00920502 %U https://u-bourgogne.hal.science/hal-00920502 %~ UNIV-BOURGOGNE %~ CNRS %~ ENSAM %~ LE2I %~ TDS-MACS %~ AGREENIUM %~ ARTS-ET-METIERS-SCIENCES-ET-TECHNOLOGIES %~ HESAM %~ HESAM-ENSAM %~ INSTITUT-AGRO