Abstract :
For a graph G the symbol G→(3,…,3r) means that in every r-colouring of the vertices of G there exists a monochromatic triangle. The triangle vertex Folkman numbers Fr(3)=min{|V(G)|:G→(3,…,3r) and cl(G)<2r} are considered. We prove that Fr(3)=2r+7, r⩾3.