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On the growth rate of chromatic numbers of finite subgraphs
Advances in Mathematics ( IF 1.5 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.aim.2020.107176
Chris Lambie-Hanson

We prove that, for every function $f:\mathbb{N} \rightarrow \mathbb{N}$, there is a graph $G$ with uncountable chromatic number such that, for every $k \in \mathbb{N}$ with $k \geq 3$, every subgraph of $G$ with fewer than $f(k)$ vertices has chromatic number less than $k$. This answers a question of Erdős, Hajnal, and Szemeredi.

中文翻译:

关于有限子图的色数增长率

我们证明,对于每个函数 $f:\mathbb{N} \rightarrow \mathbb{N}$,存在一个具有不可数色数的图 $G$,使得对于每个 $k \in \mathbb{N}$用$k \geq 3$,$G$ 的每一个少于$f(k)$ 顶点的子图的色数都小于$k$。这回答了 Erdős、Hajnal 和 Szemeredi 的问题。
更新日期:2020-08-01
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