Bipartite Turán problems via graph gluing

Abstract For graphs and , if we glue them by identifying a given pair of vertices and , what is the extremal number of the resulting graph ? In this paper, we study this problem and show that interestingly it is equivalent to an old question of Erdős and Simonovits on the Zarankiewicz problem. When are copies of a same bipartite graph and come from a same part, we prove that . As a corollary, we provide a short self‐contained disproof of a conjecture of Erdős, which was recently disproved by Janzer.