Let \(a_1,\dots,a_r\) be positive integers and \(m=1+\sum_{i=1}^r(a_i-1)\). The vertex Folkman number \(F(a_1,\dots,a_r,m-1)\) is the minimum number of vertices of a graph \(G\) such that \(K_{m-1} \not\subset G\) and for every vertex \(r\)-coloring of \(G\) there exists a monochromatic \(a_i\)-clique of color \(i\) for some \(i \in \{1,\dots,r\}\). The author proves that \(F(a_1,\dots,a_r,m-1)=m+6\) for \(p=3\) and \(m \geq 6\) and \(F(a_1,\dots,a_r,m-1)=m+7\) for \(p=4\) and \(m \geq 6\), where \(p=\max \{a_1,\dots,a_r\}\).