Let $α$ be the infinite ordinal $\omega^{\omega}$. It was proved by Chang [Ch72] that any red/blue colouring of the edges of $K_α$ there is either a red $K_α$ or a blue $K_3$.

Let m be a finite cardinal $< \omega$. Let $α$ be the infinite ordinal $\omega^{\omega}$. It was proved by Milnor that any red/blue colouring of the edges of $K_α$ there is either a red $K_α$ or a blue $K_3$. A shorter proof was found by Larson [La73]