For r≥2 and k≥K r^2 log^6(2r), the paper proves R_r(k) ≤ exp(-c k/(r^2 log^4(2r))) r^{rk}, improving the previously known multicolor Ramsey upper bound.
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New upper bound for multicolor Ramsey numbers
For r≥2 and k≥K r^2 log^6(2r), the paper proves R_r(k) ≤ exp(-c k/(r^2 log^4(2r))) r^{rk}, improving the previously known multicolor Ramsey upper bound.