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High Quality Content by WIKIPEDIA articles! In combinatorics, Ramseys theorem states that in any colouring of the edges of a sufficiently large complete graph, one will find monochromatic complete subgraphs. For 2 colours, Ramseys theorem states that for any pair of positive integers (r, s), there exists a least positive integer R(r, s) such that for any complete graph on R(r, s) vertices, whose edges are coloured red or blue, there exists either a complete subgraph on r vertices which is entirely blue, or a complete subgraph on s vertices which is entirely red. Here R(r, s) signifies an integer that depends on both r and s. It is understood to represent the smallest integer for which the theorem holds. Greek Mesolithic: Problems and Perspectives by Nena Galanidou