(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2002)
Let a_1,...,a_r be positive integers and m=_i=1^r(a_i-1)+1. For a graph G the symbol G→(a_1,...,a_r) means that in every r-colouring of the vertices of G there exists a monochromatic a_i-clique of colour i, for some i, 1 ≤ i ≤ r. In this paper we consider the graphs G→(a_1,...,a_r) (vertex Folkman graphs) with cl(G) < m - 1.