Large subgraphs without complete bipartite graphs
  In this note, we answer the following question of Foucaud, Krivelevich and Perarnau. What is the size of the largest $K_{r,s}$-free subgraph one can guarantee in every graph $G$ with $m$ edges? We also discuss the analogous problem for hypergraphs. 
David Conlon, Jacob Fox, Benny Sudakov
math.CO