We consider the distributed complexity of the (degree+1)-list coloring problem, in which each node $u$ of degree $d(u)$ is assigned a palette of $d(u)+1$ colors, and the goal is to find a proper coloring using these color palettes. The (degree+1)-list coloring problem is a natural generalization of the classical $(\Delta+1)$-coloring and $(\Delta+1)$-list coloring problems, both being benchmark problems extensively studied in distributed and parallel computing. In this paper we settle the complexity of the (degree+1)-list coloring problem in the Congested Clique model by showing that it can be solved deterministically in a constant number of rounds.

翻译：我们考虑(度+1)-列表着色问题的分布式复杂度，其中每个度为$d(u)$的节点$u$被分配一个包含$d(u)+1$种颜色的调色板，目标是利用这些调色板找到一种合适的着色方案。(度+1)-列表着色问题是经典$(\Delta+1)$-着色和$(\Delta+1)$-列表着色问题的自然推广，这两个基准问题在分布式和并行计算领域均得到广泛研究。本文通过证明该问题可在常数轮内确定性求解，确立了拥堵团模型下(度+1)-列表着色问题的复杂度。