Olivér Janzer: On the Turán number of graphs with minimum degree 3

In 1981, Erdős and Simonovits conjectured that for any bipartite graph H we have ex(n,H)=O(n3/2) if and only if H is 2-degenerate. Later, Erdős offered 250 dollars for a proof and 100 dollars for a counterexample. We disprove the conjecture by finding, for any ϵ>0, a 3-regular bipartite graph H with ex(n,H)=O(n4/3+ϵ).