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A well known conjecture of Burr and Erdos asserts that the Ramsey number $r(Q_n)$ of the hypercube $Q_n$ on $2^n$ vertices is of the order $O(2^n)$.
S. A. Burr and P. Erdős, On the magnitude of generalized Ramsey numbers for graphs, in Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I
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