On minimal Folkman graphs Original Research Article

Following the arrow notation, for a graph G and natural numbers a1,a2,…,ar we write G→(a1,a2,…,ar)v if for every coloring of the vertices of G with r colors there exists a copy of the complete graph Kai of color i for some i=1,2,…,r. We present some constructions of small graphs with this Ramsey property, but not containing large cliques. We also set bounds on the order of the smallest such graphs.