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：鉴于一个非减序 $S = (s ⁇ 1}, s ⁇ 2},\ ldots,\ ldots $, s ⁇ k}) 正数整数的美元, 以美元包装一美元包装的G$图彩色是G美元套装成 $K美元子子的折合, $V ⁇ 1 }, V ⁇ 2},\ ldots, V ⁇ k ⁇ $, 等于每1美元\leq i\leq k$, 任何两个不同的顶点 $uu$ 和 $v$ $ $ $ $V ⁇ i} 之间的距离至少是 $s ⁇ + $ +$。 在本文中, 我们研究了 $S 包装 问题 问题 。 我们证明每立方的 Halin 图形是 1, 1, 2, 3, 3美元包装的彩色。 此外, 我们证明这些图表是 1, 2, 2, 2, 2, 2, 2, 2美元 美元包装的彩色 。
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