图、超滤子和可着色性
Graphs, Ultrafilters and Colourability
摘要：
设$β$是从Set到CHaus的函子，它将每个离散集X映射到它的Stone-Cech紧化，即X上的超滤子集$β$ X。每个顶点集为V的图G自然地在V上的超滤子集$βV$上生成一个图$βG$。在下文中，我们将G和$βG$的性质联系起来。也许最引人注目的结果是G可以是可着色的当且仅当$βG$没有环。
英文摘要：
Let $β$ be the functor from Set to CHaus which maps each discrete set X to its Stone-Cech compactification, the set $β$ X of ultrafilters on X. Every graph G with vertex set V naturally gives rise to a graph $βG$ on the set $βV$ of ultrafilters on V . In what follows, we interrelate the properties of G and $βG$. Perhaps the most striking result is that G can be finitely coloured iff $βG$ has no loops.
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。
