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Erdős problem 183

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Let R(3;k)R(3;k) be the least nn such that every kk-colouring of the edges of KnK_n contains a monochromatic triangle. Determine lim⁡k→∞R(3;k)1/k\lim_{k\to\infty} R(3;k)^{1/k} (a $250 Erdős prize problem). A superexponential lower bound resolves the problem: the limit is infinite.

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Let $R(3;k)$ be the least $n$ such that every $k$-colouring of the edges of $K_n$ contains a monochromatic triangle. Determine $\lim_{k\to\infty} R(3;k)^{1/k}$ (a \$250 Erdős prize problem). A superexponential lower bound resolves the problem: the limit is infinite.

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