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 $D_A/k_A+D_B/k_B\le 1$ 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 the other due to Szab\'o and Tardos.

翻译：给定二部图 $H=(V=V_A\cup V_B,E)$，其中 $V_A$（对应地 $V_B$）中任意顶点的度数至多为 $D_A$（对应地 $D_B$）。假设存在 $V$ 的一个划分，该划分是二部划分 $V_A\cup V_B$ 的一个加细，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 $D_A/k_A+D_B/k_B\le 1$ 足以保证 $H$ 中存在一个同时为划分横截的独立顶点集，并进一步证明该条件是紧的。这一结果是关于独立横截的两个著名结果的二部加细形式，其一位于第二作者，另一个归功于 Szabó 和 Tardos。