Erdős Problem 1016

### What is the conjecture

https://www.erdosproblems.com/1016

Let $h(n)$ be minimal such that there is a graph on $n$ vertices with $n+h(n)$ edges which contains a cycle on $k$ vertices, for all $3\leq k\leq n$. Estimate $h(n)$. In particular, is it true that
$$h(n) \geq \log_2n+\log_*n-O(1),$$
where $\log_*n$ is the iterated logarithmic function?

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 Erdős Problems 1016 statement at https://www.erdosproblems.com/1016 and inspecting how formal-conjectures represents similar conjectures in Lean. The work is done when this open graph-theory conjecture, including its lower-bound question, has been added as a Lean formalization.

Written by the indexing model from the issue text.