For every fixed s > 3, the 3-uniform Ramsey number r_3(s, g_3(s)+1; t) is at least 2^{c t^{2/3}} for some c > 0, settling the last open case of the 1972 Erdős-Hajnal conjecture.
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Polynomial-to-exponential transition in 3-uniform Ramsey numbers
For every fixed s > 3, the 3-uniform Ramsey number r_3(s, g_3(s)+1; t) is at least 2^{c t^{2/3}} for some c > 0, settling the last open case of the 1972 Erdős-Hajnal conjecture.