2022/09/19 by Tarhini, Batoul, Togni, Olivier
#05C15 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2209.09135
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.