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We improve the upper bound for diagonal Ramsey numbers to R(k+1,k+1)≤exp(−c(logk)2)2kk for k≥3. To do so, we build on a quasirandomness and induction framework for Ramsey numbers introduced by Thomason and extended by Conlon, demonstrating optimal “effective quasirandomness” results about convergence of graphs. This optimality represents a natural barrier to improvement.
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Ashwin Sah (2023) studied this question.
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