This also is a special case of Ramsey's theorem, which says that for any given integer "c", any given integers "n"1...,"n""c", there is a number, "R"("n"1...,"n""c"), such that if the edges of a complete graph of order "R"("n"1...,"n""c") are coloured with "c" different colours, then for some "i" between 1 and "c", it must contain a complete subgraph of order "ni" whose edges are all colour "i". The special case above has "c" = 2 and "n"1 = "n"2 = 3.