 
Summary: 2Source Dispersers for no(1)
Entropy, and Ramsey Graphs Beating
the FranklWilson Construction
Boaz Barak
Anup Rao
Ronen Shaltiel
Avi Wigderson§
July 22, 2008
Abstract
The main result of this paper is an explicit disperser for two independent sources on n bits,
each of minentropy k = 2log10 n
, for some small absolute constant 0 > 0). Put differently,
setting N = 2n
and K = 2k
, we construct an explicit N × N Boolean matrix for which no K × K
submatrix is monochromatic. Viewed as the adjacency matrix of a bipartite graph, this gives an
explicit construction of a bipartite KRamsey graph of 2N vertices.
This improves the previous the previous bound of k = o(n) of Barak, Kindler, Shaltiel, Sudakov
and Wigderson [BKS+
05]. As a corollary, we get a construction of a 22log10 n
