可数图是多数3-可选图
Countable graphs are majority 3-choosable
摘要：
不友好划分猜想假定每一个可数图都有一个2-着色，其中每一个顶点至少有与单色边一样多的包含该顶点的双色边。这是不知道一般，但它是已知的，一个3着色与此性质总是存在的。Anholcer，Bosek和Grytczuk最近给出了这个猜想的列表着色版本，并证明了大小为4的列表存在这样的着色。我们改进了他们的结果，大小为3的列表，证明延伸到有向无圈图。我们还讨论了一些概括。
英文摘要：
The Unfriendly Partition Conjecture posits that every countable graph admits a 2-colouring in which for each vertex there are at least as many bichromatic edges containing that vertex as monochromatic ones. This is not known in general, but it is known that a 3-colouring with this property always exists. Anholcer, Bosek and Grytczuk recently gave a list-colouring version of this conjecture, and proved that such a colouring exists for lists of size 4. We improve their result to lists of size 3; the proof extends to directed acyclic graphs. We also discuss some generalisations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
