Abstract
A well known conjecture of Burr and Erdős asserts that the Ramsey number r(Qn) of the hypercube Qn on 2n vertices is of the order O(2n). In this paper, we show that r(Qn)=O(22n−cn) for a universal constant c>0, improving upon the previous best known bound r(Qn)=O(22n), due to Conlon, Fox and Sudakov.
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