Given a non-decreasing sequence $S = (s_{1}, s_{2}, \ldots , s_{k})$ of positive integers, an $S$-packing coloring of a graph $G$ is a partition of the vertex set of $G$ into $k$ subsets $\{V_{1}, V_{2}, \ldots , V_{k}\}$ such that for each $1 \leq i \leq k$, the distance between any two distinct vertices $u$ and $v$ in $V_{i}$ is at least $s_{i} + 1$. 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.

翻译：给定一个由正整数组成的非递减序列$S = (s_{1}, s_{2}, \ldots , s_{k})$，图$G$的$S$-打包染色是将$G$的顶点集划分为$k$个子集$\{V_{1}, V_{2}, \ldots , V_{k}\}$，使得对于每个$1 \leq i \leq k$，$V_{i}$中任意两个不同顶点$u$和$v$之间的距离至少为$s_{i} + 1$。本文研究三次哈林图的$S$-打包染色问题，证明每一个三次哈林图都是$(1,1,2,3)$-可打包染色的。此外，我们还证明了这类图是$(1,2,2,2,2,2)$-可打包染色的。