Abstract : 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.
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-00920502 Contributeur : Nicolas GastineauConnectez-vous pour contacter le contributeur Soumis le : jeudi 29 janvier 2015 - 19:19:31 Dernière modification le : dimanche 26 juin 2022 - 00:44:03 Archivage à long terme le : : jeudi 30 avril 2015 - 12:00:13