New bounds on the vertex Folkman number $F_v(2,2,2,3;4)$

For a graph $G$ the expression $G(a_1,\mathrm{.}\mathrm{.}\mathrm{.},a_s)$ means that for every coloring of the vertices of $G$ in $s$ colors there exists $i\in \{1,\mathrm{.}\mathrm{.}\mathrm{.},s\}$ such that there is a monochromatic $a_i$-clique of color $i$. The vertex Folkman number $F_v(a_1,\mathrm{.}\mathrm{.}\mathrm{.},a_s;q)$ is defined as $$F_v(a_1,\mathrm{.}\mathrm{.}\mathrm{.},a_s;q)=\min \{\mathrm{\mid }V(G)\mathrm{\mid }:G(a_1,\mathrm{.}\mathrm{.}\mathrm{.},a_s)and{K}_q\subseteq ̸G\}\mathrm{.}$$ In this paper we improve the known bounds on the number $F_v(2,2,2,3;4)$ by proving with the help of a computer that $20\le F_v(2,2,2,3;4)\le 22$.