A New Upper Bound for Diagonal Ramsey Numbers

Details A New Upper Bound for Diagonal Ramsey Numbers A New Upper Bound for Diagonal Ramsey Numbers

2006-07-30

arxiv.org/abs/math/0607788v1

Mathematics

Combinatorics

22 pages

Scientific paper

We prove a new upper bound for diagonal two-colour Ramsey numbers, showing
that there exists a constant $C$ such that \[r(k+1, k+1) \leq k^{- C \frac{\log
k}{\log \log k}} \binom{2k}{k}.\]

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