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?
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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.
 Piwakowski, K., and Radziszowski, S. P., Journal of Combinatorial Mathematics and Combinatorial Computing, 27:135141, 1998.

5$\begingroup$ Actually, $R(3,3,4)=30$. See dcs.gla.ac.uk/~alice/papers/ramseyConstraints2016.pdf $\endgroup$ – Julian Mar 28 '18 at 8:56