Problem 1029

Erdős Problem #1029: declared status 'open'. Formalized: no. If $R(k)$ is the Ramsey number for $K_k$, the minimal $n$ such that every $2$-colouring of the edges of $K_n$ contains a monochromatic copy of $K_k$, then$$\frac{R(k)}{k2^{k/2}}\to \infty.$$ Current best: [Sp75] Spencer, Joel, Ramsey's theorem---a new lower bound. Prize: $100. OEIS: A059442. Tags: graph theory, ramsey theory.