S -packing coloring of cubic Halin graphs
Coloration de S-packing des graphes de Halin cubiques
Résumé
Given a non-decreasing sequence S = (s1, s2, . . . , sk) of positive integers, an S-packing coloring of a graph G is a partition of the vertex set of G into k subsets {V1, V2, . . . , Vk} such that for each 1 ≤ i ≤ k, the distance between any two distinct vertices u and v in Vi is at least si + 1. In this paper, we study the problem of S-packing coloring of cubic Halin graphs, and we prove that every cubic Halin graph is (1, 1, 2, 3)-packing colorable. In addition, we prove that such graphs are (1, 2, 2, 2, 2, 2)-packing colorable.