Erdős Problem #554

declared status 'open'. Formalized: no. Let $R(G;k)$ denote the minimal $m$ such that if the edges of $K_m$ are $k$-coloured then there is a monochromatic copy of $G$. Show that$$\lim_{k\to \infty}\frac{R(C_{2n+1};k)}{R(K_3;k)}=0$$for any $n\geq 2$. Prize: no. Tags: graph theory, ramsey theory.

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