Growth rate of diagonal Ramsey numbers

Open

erdos-ramsey-growth

Statement

For the diagonal Ramsey number $R (k)$ , determine whether $lim_{k} R (k)^{1/ k}$ exists and its value. It is known that $2 \leq lim inf \leq lim sup \leq 4$ .

Current frontier

erdosproblems.com/77, OPEN. Lower bound $\sim (k / (e 2)) 2^{k /2}$ (Erdős 1947); Campos–Griffiths–Morris–Sahasrabudhe (2023) gave the first exponential upper-bound gain ( $ε \approx 2^{- 7}$ ), since lowered to $R (k) \leq 3.799 2^{k}$ by Gupta–Ndiaye–Norin–Wei (2024).

When this counts as solved

VALUE-DETERMINATION

PROOF_COMPLETE for the limit and its value with matching bounds. BREAKTHROUGH for raising the lower-bound base above $2$ , lowering the upper base below the current best $3.7992$ , or proving the limit exists.

Classification

Value-determination

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