User:Pmanderson/Ramsey

G127 is a graph on 127 vertices, identified with the numbers 0 through 126, with 2667 edges, in which an edge is placed between two vertices i, j, whenever j &minus; i = a3, meaning j &minus; i is a cubic residue.

G127 is a 42-regular graph, not containing any four-vertex clique. It was studied by Jonathan Cole and C.P. Knerr with the aim of proving that every partition of its edges into two subgraphs must have a triangle in one or the other of the subgraphs.