SOLVED
Let $k\geq 2$ and $l\geq 3$. Is there a graph $G$ which contains no $K_{l+1}$ such that every $k$-colouring of the edges of $G$ contains a monochromatic copy of $K_l$?
A question of Erdős and Hajnal. Folkman
[Fo70] proved this when $k=2$. The case for general $k$ was proved by Nešetřil and Rödl
[NeRo76].
See [582] for a special case.
