List colouring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening of this problem, where instead of one list-colouring, we seek many in parallel. Our explorations have uncovered a potentially rich seam of interesting problems spanning chromatic graph theory. Given a $k$-list-assignment $L$ of a graph $G$, which is the assignment of a list $L(v)$ of $k$ colours to each vertex $v\in V(G)$, we study the existence of $k$ pairwise-disjoint proper colourings of $G$ using colours from these lists. We may refer to this as a \emph{list-packing}. Using a mix of combinatorial and probabilistic methods, we set out some basic upper bounds on the smallest $k$ for which such a list-packing is always guaranteed, in terms of the number of vertices, the degeneracy, the maximum degree, or the (list) chromatic number of $G$. (The reader might already find it interesting that such a minimal $k$ is well defined.) We also pursue a more focused study of the case when $G$ is a bipartite graph. Our results do not yet rule out the tantalising prospect that the minimal $k$ above is not too much larger than the list chromatic number. Our study has taken inspiration from study of the strong chromatic number, and we also explore generalisations of the problem above in the same spirit.

翻译：列表染色是图论中一个影响深远的经典课题。我们首次研究了该问题的一个自然强化版本：不再寻求单一列表染色，而是并行寻找多个列表染色。我们的探索揭示了一个可能富含有趣问题的广阔领域，其核心跨越染色图论。给定图$G$的一个$k$-列表赋值$L$（即对每个顶点$v\in V(G)$分配一个包含$k$种颜色的列表$L(v)$），我们研究是否存在$k$个两两不相交的$G$的恰当染色，且每个染色所使用的颜色均来自这些列表。我们将此称为"列表打包"。结合组合方法与概率方法，我们建立了保证此类列表打包存在的最小$k$的基本上界，这些上界取决于$G$的顶点数、退化度、最大度或（列表）色数。（读者或许会发现，这种最小$k$的良好定义本身已颇具趣味。）我们进一步针对$G$为二分图的情形进行了集中研究。目前的结果尚无法排除一个诱人的可能性：上述最小$k$可能不会比列表色数大太多。本研究从强色数的研究中汲取灵感，并以相同思路探索了该问题的若干推广形式。