On the 2-coloring diagonal vertex Folkman numbers with minimal possible clique number - Kolev, Nikolay; Nenov, Nedyalko (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2008)
For a graph $G$ the symbol $G\xrightarrow{v}(p,p)$ means that in every 2-coloring of the vertices of $G$, there exists a monochromatic $p$-qlique. The vertex diagonal Folkman numbers $$ F_v(p,p;p+1)=\min\{|V(G)| : G\xrightarrow{v}(p,p) \;and\; K_{p+1} ot\subset G \} $$ are considered. We prove that $F_v(p,p;p+1)≤\frac{13}{12}p!,\,\;p≥ 4$.