Multiplicity of triangles in cocktail party graphs Original Research Article

If F and G are graphs, define M(G,F) to be the minimum number of monochromatic G that occur in any 2-colouring of the edges of F and call it as the multiplicity of G in F. In this paper we prove that M(K3,G2n) = 8M(K3,Kn) for all n where G2n is the cocktail party graph on 2n vertices. Lower bounds are shown to be sharp by explicit colouring schemes.