... New upper bound for a class of vertex Folkman numbersN. KolevDepartment of AlgebraFaculty of Mathematics and Informatics“St. Kl. Ohridski” University of So a 5 J. Bourchier blvd, 1164 So a BULGARIAN. ... ≥ max {a 1, ,a r}. Folkman [3] provedthat there exists a graph G such that G → (a 1, ,a r)andcl(G)=max {a 1, ,a r}.ThereforeF (a 1, ,a r; q) exists if and only if q>max {a 1, ,a r}. ... SerdicaBulgaricae math. publicationes 9, 1983, 161–167 (in Russian).[8] N. Nenov, On a class of vertex Folkman graphs, Annuaire Univ. So a Fac. Math.Inform. 94, 2000, 15–25.[9] K. Piwakowski, S. Radziszowski,...