Erdős Problem 1032

### What is the conjecture

https://www.erdosproblems.com/1032

We say that a graph is $4$-chromatic critical if it has chromatic number $4$, and removing any edge decreases the chromatic number to $3$.

Is there, for arbitrarily large $n$, a $4$-chromatic critical graph on $n$ vertices with minimum degree $\gg n$?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reading the conjecture at https://www.erdosproblems.com/1032 and then inspect the formal-conjectures repository for how graph-theory conjectures are represented in Lean. The issue names no target file or test, so determine the appropriate entry point and formalization scope before beginning. Done means the stated Erdős Problem 1032 conjecture has been added in the repository's expected form.

Written by the indexing model from the issue text.