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Combinatorics · Oct 6, 2026

Sharp logarithmic exponents for off-diagonal Ramsey numbers

For every fixed integer s ≥ 5, proves r(s,t)=ts−1/(log⁡t)s−2+o(1)r(s,t)=t^{s-1}/(\log t)^{s-2+o(1)} as t→∞t\to\infty, determining the logarithmic exponent and matching the classical upper bound at that scale. Here r(s,t)r(s,t) is the least number of vertices forcing an s-clique or a t-vertex independent set.

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