Improved bounds for the Erdős-Rogers $(s,s+2)$-problem

Oliver Janzer, Benny Sudakov

For $2\le s<t$, the Erdős-Rogers function $f_{s,t}(n)$ measures how large a $K_s$-free induced subgraph there must be in a $K_t$-free graph on $n$ vertices. There has been an exte…