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Published September 2009 | Submitted
Journal Article Open

A new upper bound for diagonal Ramsey numbers


We prove a new upper bound for diagonal two-colour Ramsey numbers, showing that there exists a constant C such that r(k + 1, k + 1) ≤ k^[-C log k/(log log k (2k_k).

Additional Information

© 2009 Princeton University. Received 11 July 2006; revised 14 November 2007. The author is kindly supported by a grant from St John's College, Cambridge. I would like to thank Béla Bollobás, Tim Gowers, Ben Green and Tom Sanders for their advice and encouragement.

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August 19, 2023
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