In his 1947 paper that inaugurated the probabilistic method, Erdös proved the existence of 2\log{n}-Ramsey graphs on n vertices. Matching Erdös' result with a constructive proof is a central problem in combinatorics, that has gained a significant attention in the literature. The state of the art result was obtained in the celebrated paper by Barak, Rao, Shaltiel and Wigderson [Ann. Math'12], who constructed a 2^{2^{(\log\log{n})^{1-\alpha}}}-Ramsey graph, for some small universal constant \alpha > 0.
In this work, we significantly improve the result of Barak et al. and construct 2^{(\log\log{n})^c}-Ramsey graphs, for some universal constant c. In the language of theoretical computer science, our work resolves the problem of explicitly constructing two-source dispersers for polylogarithmic entropy.