An example of a 16-vertex Folkman edge (3,4)-graph without 8-cliques

Abstract

In [6] we computed the edge Folkman number $F(3,4;8)=16$. There we used and announced without proof that in any blue-red coloring of the edges of the graph $K_1+C_5+C_5+C_5$ there is either a blue 3-clique or red 4-clique. In this paper we give a detailed proof of this fact.