[formula omitted]-packing coloring of cubic Halin graphs

Abstract

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.