On the growth rate of chromatic numbers of finite subgraphs

Chris Lambie-Hanson

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arXiv · 1902.08177

On the growth rate of chromatic numbers of finite subgraphs

Chris Lambie-Hanson

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Abstract

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 Erd\H{o}s, Hajnal, and Szemeredi.

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Chris Lambie-Hanson. 2019-02-21. On the growth rate of chromatic numbers of finite subgraphs. https://arxiv.org/abs/1902.08177

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