Problem Statement
Let $\delta>0$. If $n$ is sufficiently large and $G$ is a graph on $n$ vertices with no $K_{2,2,2}$ and at least $\delta n^2$ edges then $G$ contains an independent set of size $\gg_\delta n$.
Categories:
Graph Theory Turan Number
Progress
A problem of Erdős, Hajnal, Sós, and Szemerédi, who could prove this is true for $\delta>1/8$.See also [533] and the entry in the graphs problem collection.
Source: erdosproblems.com/579 | Last verified: January 15, 2026