Weak multiplicative Ramsey Diagonal Conjecture

Prove that for every positive integers \(s,t,k\) satisfying \(st\le k^2\), the Ramsey numbers obey \(R(s,t)\le R(k,k)\).

Background

The weak multiplicative Ramsey Diagonal Conjecture is introduced as a conjectural bridge between off-diagonal and diagonal Ramsey numbers. If true, it would allow bounds on general R(s,t)R(s,t) to be controlled by diagonal values R(k,k)R(k,k) whenever st≤k2st\le k^2.

The paper proves that this conjecture, together with existence of the diagonal Ramsey growth limit, determines the asymptotic constant in f(n)f(n).

References

For every $s, t, k \in $ such that $st k2$ we have that \begin{equation*} R(s,t) R(k, k). \end{equation*}

— On the maximum ratio between chromatic number and clique number  (2512.16062 - Araujo et al., 18 Dec 2025) in Conjecture 1, Section 1, Introduction