English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In his 1947 paper that inaugurated the probabilistic method, Erd\H{o}s provedthe existence of $2\log{n}$-Ramsey graphs on $n$ vertices. Matching Erd\H{o}s'result with a constructive proof is a central problem in combinatorics, thathas gained a significant attention in the literature. The state of the artresult was obtained in the celebrated paper by Barak, Rao, Shaltiel andWigderson [Ann. Math'12], who constructed a$2^{2^{(\log\log{n})^{1-\alpha}}}$-Ramsey graph, for some small universalconstant $\alpha > 0$.  In this work, we significantly improve the result of Barak~\etal andconstruct $2^{(\log\log{n})^c}$-Ramsey graphs, for some universal constant $c$.In the language of theoretical computer science, our work resolves the problemof explicitly constructing two-source dispersers for polylogarithmic entropy.

Two-Source Dispersers for Polylogarithmic Entropy and Improved Ramsey Graphs