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