Erdős Problem 883

### What is the conjecture

https://www.erdosproblems.com/883

For $A\subseteq \\{1,\ldots,n\\}$ let $G(A)$ be the graph with vertex set $A$, where two integers are joined by an edge if they are coprime.

Is it true that if
$$\lvert A\rvert >\lfloor\tfrac{n}{2}\rfloor+\lfloor\tfrac{n}{3}\rfloor-\lfloor\tfrac{n}{6}\rfloor$$
then $G(A)$ contains all odd cycles of length $\leq \frac{n}{3}+1$?

Is it true that, for every $\ell\geq 1$, if $n$ is sufficiently large and
$$\lvert A\rvert >\lfloor\tfrac{n}{2}\rfloor+\lfloor\tfrac{n}{3}\rfloor-\lfloor\tfrac{n}{6}\rfloor$$
then $G(A)$ must contain a complete $(1,\ell,\ell)$ triparite graph on $2\ell+1$ vertices?

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 linked Erdős Problem 883 statement and inspect existing formalized conjectures in the repository for the appropriate entry point. Done means the conjecture is added in Lean according to the repository's conventions; the issue names no target file, test, or implementation path.

Written by the indexing model from the issue text.