论文标题
每个亚地铁的多式图都是$（1,2^7）$ - 包装边缘可着色
Every subcubic multigraph is $(1,2^7)$-packing edge-colorable
论文作者
论文摘要
For a non-decreasing sequence $S = (s_1, \ldots, s_k)$ of positive integers, an $S$-packing edge-coloring of a graph $G$ is a decomposition of edges of $G$ into disjoint sets $E_1, \ldots, E_k$ such that for each $1 \le i \le k$ the distance between any two distinct edges $e_1, e_2 \在e_i $中至少为$ s_i+1 $。首先，加斯托诺（Gastineau）和托格尼（Togni）从其顶点对应物中概括了$ s $包装的边缘颜色的概念。他们表明，有一些亚地带图不是$（1,2,2,2,2,2,2,2）$ - 包装（缩写为$（1,2^6）$ - 包装）边缘色，并询问了每个亚立方图是否为$（1,2^7）$（1,2^7）$ - 包装边缘的edge enge endecolable。最近，Hocquard，Lajou和Lužar表明，每个亚地块的图都是$（1,2^8）$ - 包装边缘色，每$ 3 $ - edge-edge可着色的亚地带图为$（1,2^7）$ - 包装边缘可填充。此外，他们还猜想每个亚立方图都是$（1,2^7）$ - 包装边缘。 在本文中，我们确认了hocquard，lajou和lužar的猜想，并将其扩展到多编码。
For a non-decreasing sequence $S = (s_1, \ldots, s_k)$ of positive integers, an $S$-packing edge-coloring of a graph $G$ is a decomposition of edges of $G$ into disjoint sets $E_1, \ldots, E_k$ such that for each $1 \le i \le k$ the distance between any two distinct edges $e_1, e_2 \in E_i$ is at least $s_i+1$. The notion of $S$-packing edge-coloring was first generalized by Gastineau and Togni from its vertex counterpart. They showed that there are subcubic graphs that are not $(1,2,2,2,2,2,2)$-packing (abbreviated to $(1,2^6)$-packing) edge-colorable and asked the question whether every subcubic graph is $(1,2^7)$-packing edge-colorable. Very recently, Hocquard, Lajou, and Lužar showed that every subcubic graph is $(1,2^8)$-packing edge-colorable and every $3$-edge colorable subcubic graph is $(1,2^7)$-packing edge-colorable. Furthermore, they also conjectured that every subcubic graph is $(1,2^7)$-packing edge-colorable. In this paper, we confirm the conjecture of Hocquard, Lajou, and Lužar, and extend it to multigraphs.
