Erdős Problem 1091

### What is the conjecture

https://www.erdosproblems.com/1091

Let $G$ be a $K_4$-free graph with chromatic number $4$. Must $G$ contain an odd cycle with at least two diagonals? More generally, is there some $f(r)\to \infty$ such that every graph with chromatic number $4$, in which every subgraph on $\leq r$ vertices has chromatic number $\leq 3$, contains an odd cycle with at least $f(r)$ diagonals?

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 with the Erdős Problem 1091 statement and its linked page, then inspect how this repository represents existing formalized conjectures. The issue names no target file or entry point, so first identify the appropriate location and project conventions; done means adding a formal statement of the conjecture to the collection.

Written by the indexing model from the issue text.