How much is known about the Ramsey number R(3,3,4)? There is a trivial upper bound of 34, but are any tighter bounds known?


According to the reference 1 below to earlier work of the authors in this paper here, it is known that $$ 30\leq R(3,3,4)\leq 31 $$

Edit: A more recent paper, by Codish, Frank, Itzhakov and Miller, available here has shown that $R(3,3,4)=30.$ Thanks to @Julian.

  1. Piwakowski, K., and Radziszowski, S. P., Journal of Combinatorial Mathematics and Combinatorial Computing, 27:135-141, 1998.
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