发表机构
Shaoxing University; Zhejiang Normal University（绍兴大学; 浙江师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文改进了$K_t$-无minor图的列表色数上界，证明了每个$K_t$-无minor图是$O(t\log\log t)$-可选择的，改进了先前的结果。
AI 中文摘要
关于每个$K_t$-无minor图是否为$O(t)$-可选择的这一问题仍未解决。Postle证明了每个$K_t$-无minor图的choice number为$O(t(\log\log t)^6)$。在一篇早期版本的论文末尾，该论文确立了$K_t$-无minor图的色数的$O(t\log\log t)$界，Delcourt和Postle指出，他们的方法结合Postle的早期技术，可得出choice number的$O(t(\log\log t)^2)$界。在本文中，我们首先证明每个$n$顶点$K_t$-无minor图的choice number为$O(t\log(2+n/t))$。以此界作为关键成分，我们遵循Delcourt和Postle概述的方法，证明每个$K_t$-无minor图都是$O(t\log\log t)$-可选择的。
英文摘要
It remains open whether every $K_t$-minor-free graph is $O(t)$-choosable. Postle proved that every $K_t$-minor-free graph has choice number $O(t(\log\log t)^6)$. At the end of an earlier version of a paper establishing an $O(t\log\log t)$ bound on the chromatic number of $K_t$-minor-free graphs, Delcourt and Postle remarked that their methods, combined with Postle's earlier techniques, yield an $O(t(\log\log t)^2)$ bound on the choice number. In this paper, we first prove that every $n$-vertex $K_t$-minor-free graph has choice number $O(t\log(2+n/t))$. Using this bound as a key ingredient, we follow the approach outlined by Delcourt and Postle to prove that every $K_t$-minor-free graph is $O(t\log\log t)$-choosable.
Comments23 pages, 2 figures
