Erdős Problem 611

### What is the conjecture

https://www.erdosproblems.com/611

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).

Is it true that if all maximal cliques in $G$ have at least $cn$ vertices then $\tau(G)=o_c(n)$?

Similarly, estimate for $c>0$ the minimal $k_c(n)$ such that if every maximal clique in $G$ has at least $k_c(n)$ vertices then $\tau(G)<(1-c)n$.

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 Erdős Problem 611 at the linked erdosproblems.com page, then inspect existing formalized conjectures in this repository for the expected statement structure and entry points. Done means adding a Lean formalization of the stated conjecture to the collection, with the relevant definitions and quantifiers represented precisely.

Written by the indexing model from the issue text.