Given a bipartite graph $H=(V=V_A\cup V_B,E)$ in which any vertex in $V_A$ (resp.~$V_B$) has degree at most $D_A$ (resp.~$D_B$), suppose there is a partition of $V$ that is a refinement of the bipartition $V_A\cup V_B$ such that the parts in $V_A$ (resp.~$V_B$) have size at least $k_A$ (resp.~$k_B$). We prove that the condition $D_A/k_B+D_B/k_A\le 1$ is sufficient for the existence of an independent set of vertices of $H$ that is simultaneously transversal to the partition, and show moreover that this condition is sharp. This result is a bipartite refinement of two well-known results on independent transversals, one due to the second author and the other due to Szab\'o and Tardos.

翻译：设 $H=(V=V_A\cup V_B,E)$ 是一个二分图，其中 $V_A$（对应地，$V_B$）中任意顶点的度数不超过 $D_A$（对应地，$D_B$）。假设 $V$ 存在一个划分，该划分是二分划分 $V_A\cup V_B$ 的加细，使得 $V_A$（对应地，$V_B$）中的部分大小至少为 $k_A$（对应地，$k_B$）。我们证明条件 $D_A/k_B+D_B/k_A\le 1$ 足以保证 $H$ 中存在一个独立集，该独立集同时是该划分的横截，并进一步证明该条件是最优的。这一结果是对关于独立横截的两个著名结论（一个来自第二作者，另一个来自 Szabó 和 Tardos）的二分细化。