New Upper Bounds for the Classical Ramsey Numbers $R(4,4,4)$, $R(3,4,5)$ and $R(3,3,6)$

Luis Boza

The inequality \[ R(k_1,\ldots,k_r)\le 2-r+\sum_{i=1}^r R(k_1,\ldots,k_{i-1},k_i-1,k_{i+1},\ldots,k_r) \] is well known, and it is strict whenever the right-hand side and at least…