(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2004)
For the Ramsey number R(p_1,…,p_r), r≥2, we prove that \[ R(p_1,…,p_r) > ( R(p_1,…,p_s)-1) ( R(p_s+1,…,p_r)-1), \] s{1,…,r-1}. This inequality generalizes a result obtained by Robertson (Theorem 1) and improves the lower bounds for some Ramsey numbers.