Abstract: | Let G be a graph and a1,…,ar be positive integers. The symbol G→(a1,…,ar) denotes that in every r-coloring of the vertex set V(G) there exists a monochromatic ai-clique of color i for some i∈{1,…,r}. The vertex Folkman numbers F(a1,…,ar;q)=min{|V(G)|:G→(a1,…,ar) and Kq?G} are considered. Let ai, bi, ci, i∈{1,…,r}, s, t be positive integers and ci=aibi, 1?ai?s,1?bi?t. Then we prove that F(c1,c2,…,cr;st+1)?F(a1,a2,…,ar;s+1)F(b1,b2,…,br;t+1). |