We give an approximate Menger-type theorem for when a graph $G$ contains two $X-Y$ paths $P_1$ and $P_2$ such that $P_1 \cup P_2$ is an induced subgraph of $G$. More generally, we prove that there exists a function $f(d) \in O(d)$, such that for every graph $G$ and $X,Y \subseteq V(G)$, either there exist two $X-Y$ paths $P_1$ and $P_2$ such that the distance between $P_1$ and $P_2$ is at least $d$, or there exists $v \in V(G)$ such that the ball of radius $f(d)$ centered at $v$ intersects every $X-Y$ path.

翻译：我们给出一个近似的Menger型定理，该定理探讨了图$G$中包含两条$X-Y$路径$P_1$和$P_2$且$P_1 \cup P_2$是$G$的导出子图的情形。更一般地，我们证明存在一个函数$f(d) \in O(d)$，使得对于任意图$G$和$X,Y \subseteq V(G)$，要么存在两条$X-Y$路径$P_1$和$P_2$使得$P_1$与$P_2$之间的距离至少为$d$，要么存在顶点$v \in V(G)$使得以$v$为中心、半径为$f(d)$的球与每条$X-Y$路径相交。