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Published March 2012 | Submitted
Journal Article Open

On the Ramsey multiplicity of complete graphs


We show that, for n large, there must exist at least (n^t)/(C^((1+o(1))t^2)) monochromatic K_(t)s in any two-colouring of the edges of K_n, where C ≈ 2.18 is an explicitly defined constant. The old lower bound, due to Erdős [2], and based upon the standard bounds for Ramsey's theorem, is (n^t)/(4^((1+o(1))t^2)).

Additional Information

© 2012 János Bolyai Mathematical Society and Springer Verlag. Received 30 November 2007; first online 06 June 2012. The author is supported by a research fellowship at St John's College, Cambridge, but was also supported for part of the time that this work was being carried out by the MRTN-CT-2004-511953 project at the Alfréd Rényi Institute of Mathematics in Budapest.

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