The bipartite graph gluing conjecture for extremal numbers

Let $H_1$ and $H_2$ be bipartite graphs, and let $u \in V(H_1)$ and $v \in V(H_2)$. Denote by $H_1^u \odot H_2^v$ the graph obtained by identifying $u$ and $v$. The function $\mathrm{ex}(n,H)$ is the maximum number of edges in an $n$-vertex graph containing no copy of $H$.

The bipartite graph gluing conjecture. One has

$$\mathrm{ex}(n,H_1^u \odot H_2^v)=\Theta\bigl(\mathrm{ex}(n,H_1)+\mathrm{ex}(n,H_2)\bigr).$$

This conjecture proposes that gluing two bipartite graphs at one vertex preserves, up to order of magnitude, the combined extremal scale of the two constituent graphs. The paper proves important special cases and establishes equivalence with the corresponding Zarankiewicz conjecture, but the general statement is presented as open.