论文标题
$ s $ - 立方哈林图的包装着色
$S$-Packing Coloring of Cubic Halin Graphs
论文作者
论文摘要
给定一个非交换序列$ s =（s_ {1}，s_ {2}，\ ldots，s_ {k}）$的正整数，图$ g $的$ s $包装着色是$ g $ g $ g $ g $ g $ g $ k $ k $ subsets $ \ \ s $ \ \ \ \ \ v_ v _ v_ {1}的$ g $ g $ g $ g $ g $的分区v_ {k} \} $使得对于每个$ 1 \ leq i \ leq k $，在$ v_ {i} $中任意两个不同的顶点$ u $和$ v $之间的距离至少是$ s_ {i} + 1 $。在本文中，我们研究了$ s $ a $包装的颜色的问题，并且我们证明，每个立方Halin图都是$（1,1,2,3）$ - 包装可着色。此外，我们证明了此类图为$（1,2,2,2,2,2）$ - 包装可着色。
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.
