Erdős Problem 739

### What is the Erdős problem?

https://www.erdosproblems.com/739

Let $\mathfrak{m}$ be an infinite cardinal and $G$ be a graph with chromatic number $\mathfrak{m}$. Is it true that, for every infinite cardinal $\mathfrak{n}< \mathfrak{m}$, there exists a subgraph of $G$ with chromatic number $\mathfrak{n}$?

Status: open

### Choose either option
- [x] I plan on adding this Erdős problem to the repository
- [ ] This issue is up for grabs: I would like to see this Erdős problem added by somebody else

Read the Erdős Problems entry at https://www.erdosproblems.com/739 and inspect existing Erdős problem formalizations in the repository before choosing an entry point. The work is done when the stated graph-theoretic conjecture has a suitable formal statement and the repository accepts it through its Lean checks.

Written by the indexing model from the issue text.