A graph G contains another graph H as an immersion if H can be obtained from a subgraph of G by splitting off edges and removing isolated vertices. In this paper, we prove an edge-variant of the Erdős-Pósa property with respect to the immersion containment in 4-edge-connected graphs. More precisely, we prove that for every graph H, there exists a function f such that for every 4-edge-connected graph G, either G contains k pairwise edge-disjoint subgraphs each containing H as an immersion, or there exists a set of at most $f(k)$ edges of G intersecting all such subgraphs. This theorem is best possible in the sense that the 4-edge-connectivity cannot be replaced by the 3-edge-connectivity.

图G包含另一个图H作为浸入，如果H可以从G的子图中通过分割边和移除孤立顶点获得。在本文中，我们证明了 Erdős-Pósa 属性关于 4 边连通图中的浸入式包含的边变体。更准确地说，我们证明对于每个图H，存在一个函数f使得对于每个 4 边连接的图G，要么G包含k 个成对边不相交的子图，每个子图都包含H作为浸入最多$F(克)$G 的边与所有这些子图相交。这个定理在 4 边连接不能被 3 边连接代替的意义上是最好的。