论文标题
一个简短的证明，表明任何图的列表包装数量都很好
A Short Proof that the List Packing Number of any Graph is Well Defined
论文作者
论文摘要
列表包装是一个在2021年引入的概念（Cambie等人）。图$ g $的列表包装号，表示为$χ_ {\ ell}^*（g）$，是$ k $的最低$ k $，因此对于任何列表分配$ l $，每个顶点分配$ k $ colors of $ g $，$ k $ l $ l $ g $ g $ g $ g $ g $ g $，$ g $，$ g $，$ g，$ g，$ \ ld proplast f _ f _1， $ f_i（v）\ neq f_j（v）$ nesh $ 1 \ leq i <j \ leq k $和in v（g）$中的$ v \ $ v \ $。我们提供了一个简短的证明，即对于任何图形$ g $，$χ_ {\ ell}^*（g）\ leq | v（g）| $。有趣的是，我们的证明利用了加尔文（Galvin）著名的结果，即任何两部分多编码的列表列表的列表都等于其色数。
List packing is a notion that was introduced in 2021 (by Cambie et al.). The list packing number of a graph $G$, denoted $χ_{\ell}^*(G)$, is the least $k$ such that for any list assignment $L$ that assigns $k$ colors to each vertex of $G$, there is a set of $k$ proper $L$-colorings of $G$, $\{f_1, \ldots, f_k \}$, with the property $f_i(v) \neq f_j(v)$ whenever $1 \leq i < j \leq k$ and $v \in V(G)$. We present a short proof that for any graph $G$, $χ_{\ell}^*(G) \leq |V(G)|$. Interestingly, our proof makes use of Galvin's celebrated result that the list chromatic number of the line graph of any bipartite multigraph equals its chromatic number.
