ON THE VERTEX FOLKMAN NUMBERS F_v(2,...,2_R;R-1) and F_v(2,...,2_R;R-2) - Nenov, Nedyalko (Ann. Sofia Univ. Fac. Math. and Inf., 2013)
For a graph G the symbol Gv→(a_1,...,a_r) means that in every r-coloring of the vertices of G for some i{1,2,...,r} there exists a monochromatic a_i-clique of color i. The vertex Folkman numbers \[F_v(a_1,...,a_r_r;q) ={|V(G)|:Gv→(a_1,...,a_r) and K_q subseteq G}\] are considered. We prove that \[F_v(2,...,2_r;r-1) = r + 7, r ≥ 6 and F_v(2,...,2_r;r-2) = r + 9, r ≥ 8.\]