Erdős Problem 667

### What is the conjecture

https://www.erdosproblems.com/667

Let $p,q\geq 1$ be fixed integers. We define $H(n)=H(N;p,q)$ to be the largest $m$ such that any graph on $n$ vertices where every set of $p$ vertices spans at least $q$ edges must contain a complete graph on $m$ vertices.
Is
$$c(p,q)=\liminf \frac{\log H(n)}{\log n}$$
a strictly increasing function of $q$ for $1\leq q\leq \binom{p-1}{2}+1$?

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 conjecture statement and linked description at https://www.erdosproblems.com/667, then inspect the formal-conjectures repository for the relevant conventions. No file, test, or entry point is named in the issue; done means adding a formalized statement for Erdős Problem 667.

Written by the indexing model from the issue text.