Two-Source Dispersers for Polylogarithmic Entropy and Improved Ramsey Graphs [article]

Gil Cohen
2015 arXiv   pre-print
In his 1947 paper that inaugurated the probabilistic method, Erdős proved the existence of 2n-Ramsey graphs on n vertices. Matching Erdős' 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^(n)^1-α-Ramsey graph, for some small universal constant α > 0. In this work, we
more » ... ntly improve the result of Barak and construct 2^(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.
arXiv:1506.04428v1 fatcat:bnla4jwtuje55c62rdinrcboqm