Graph form of the Balog-Szemerédi-Gowers theorem
= Graph form of the Balog-Szemerédi-Gowers theorem
There are absolute $c,C>0$ such that finite sets $A,B$ of size $n$, a <bipartite graph> of density at least $\delta$, and a <restricted sumset> of size at most $Kn$ yield subsets $A',B'$ with $|A'|,|B'|\geq c\delta^Cn$ and $|A'+B'|\leq C\delta^{-C}K^Cn$. A graph formed by popular representations of sums turns this into the usual large-<additive energy> form of the <Balog-Szemerédi-Gowers theorem>.