发表机构
University of Warwick; University of Science and Technology of China; University of Washington; University of Cologne（华威大学; 中国科学技术大学; 华盛顿大学; 科隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了通用r-均匀超图的调色板稀疏化定理，确定了其着色所需列表大小的渐近紧界，为超图着色问题提供了关键的理论结果。
AI 中文摘要
我们证明了通用r-均匀超图的调色板稀疏化定理。对于所有足够大的n、所有r≥3以及所有α≥7.1，我们证明n个顶点、最大度为Δ的r-均匀超图，大概率可从大小为⌈αΔ^(1/(r-1))⌉的环境调色板中独立抽样得到的大小为O(√log n)的列表进行着色，√log n的依赖关系是渐近紧的。
英文摘要
For every fixed $k\ge2$, we give a randomized one-pass insertion-only algorithm that colors an $n$-vertex $k$-uniform hypergraph of maximum degree $Δ$ with $O(Δ^{1/(k-1)})$ colors using $\widetilde O_k(n)$ bits of working memory. As a graph-theoretic result of independent interest, we also prove a tight palette-sparsification theorem for general uniform hypergraphs. Independently sampled lists of $Θ(\sqrt{\log n})$ colors from a palette of size $O(Δ^{1/(k-1)})$ preserve colorability with high probability; the list-size dependence is asymptotically optimal. These results extend to bounded-rank hypergraphs. We complement the algorithm with a deterministic lower bound: for every fixed polylogarithmic semi-streaming space bound, there are polylogarithmic values of $Δ$ for which any deterministic one-pass algorithm requires $\exp(Δ^{Ω(1)})$ colors.
Comments25 pages. This revision merges the original manuscript with independent work by Czumaj, Peng, and Sohler
