Let $\epsilon > 0$ and let $n$ be sufficiently large depending on $\epsilon$. Is there a graph on $n$ vertices with at least $n^2/8$ many edges which contains no $K_4$, such that the largest independent set has size at most $\epsilon n$?

Let $\epsilon > 0$ and let $n$ be sufficiently large depending on $\epsilon$. Is there a graph on $n$ vertices with at least $n^2/8$ many edges which contains no $K_4$, such that the largest independent set has size at most $\epsilon n$?

This is true, as proved by Fox, Loh, and Zhao [FLZ15].