LOWER BOUNDS FOR SOME RAMSEY NUMBERS

Abstract

For the Ramsey number $R(p_1,\dots ,p_r)$, $r\ge 2$, we prove that $$R(p_1,\dots ,p_r)>(R(p_1,\dots ,p_s)-1)(R(p_{s+1},\dots ,p_r)-1),$$ $s\in \{1,\dots ,r-1\}$. This inequality generalizes a result obtained by Robertson (Theorem 1) and improves the lower bounds for some Ramsey numbers.