Aharoni and Howard's rainbow matching conjecture

Let $\mathcal{G}=\{G_1,\ldots,G_t\}$ be a family of $t$ bipartite graphs, and let $\Delta$ be a bound such that $\Delta(G_i)\leq \Delta$ for every $i$. Aharoni and Howard's rainbow matching conjecture. If

$$e(G_i)>(t-1)\Delta$$

for every $i$, then $\mathcal{G}$ admits a rainbow matching. The conjecture concerns a common matching using one edge from each graph; the source does not specify whether it has been resolved.