Finding Large p-Colored Diameter Two Subgraphs

Abstract.

Given a coloring of the edges of the complete graph K on n vertices in k colors, a p-colored subgraph of K _n is any subgraph whose edges only use colors from some p element set. We show for k≥1 and k\2≤p≤k that there is always a p-colored diameter two subgraph of K _n containing at least vertices and that this is best possible up to an additive constant l satisfying 0≤l<k\2.