Erdős Problem #924

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 $K_l$?

#924: [Er69b][Er75b]

graph theory | ramsey theory

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 and [966] for an arithmetic analogue.

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