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

Abstract

For a graph $G$ the expression $G\stackrel{v}{\to }(a_1,...,a_s)$ means that for every coloring of the vertices of $G$ in $s$ colors there exists $i\in \{1,...,s\}$ such that there is a monochromatic $a_i$-clique of color $i$. The vertex Folkman number $F_v(a_1,...,a_s;q)$ is defined as $$F_v(a_1, ..., a_s; q) = \min\{\vert V(G) \vert : G \overset{v}{\rightarrow} (a_1, ..., a_s) \mbox{ and } K_q \not\subseteq G\}.$$ 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 $20\le F_v(2,2,2,3;4)\le 22$.

References in corpus (4)

• The edge Folkman number $F_e(3,3;4)$ is greater than 19
• The vertex Folkman numbers $F_v(a_1,...,a_s;m-1)=m+9$, if $\max \{a_1,...,a_s\}=5$
• On the Vertex Folkman Numbers $F_v(2,...,2;q)$
• On The Vertex Folkman Numbers $F_v(\underset{r}{\underbrace{2,...,2}};r-1)$ and $F_v(\underset{r}{\underbrace{2,...,2}};r-2)$%