Erdős Problem 610

### What is the conjecture

https://www.erdosproblems.com/610

For a graph $G$ let $\tau(G)$ denote the minimal number of vertices that include at least one from each maximal clique of $G$ (sometimes called the clique transversal number).

Estimate $\tau(G)$. In particular, is it true that if $G$ has $n$ vertices then
$$\tau(G) \leq n-c\sqrt{n\log n}$$
for some absolute constant $c>0$?

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

Read the linked Erdős Problems page to understand the conjecture and its definitions. No Lean file, test, or entry point is named in the issue, so identify the appropriate location in this repository before formalizing the statement; done means the conjecture has been added as a Lean formalization.

Written by the indexing model from the issue text.