We extend Edmonds’ Branching Theorem to locally finite infinite digraphs. As examples of Oxley or Aharoni and Thomassen show, this cannot be done using ordinary arborescences, whose underlying graphs are trees. Instead we introduce the notion of pseudo-arborescences and prove a corresponding packing result. Finally, we verify some tree-like properties for these objects, but give also an example that their underlying graphs do in general not correspond to topological trees in the Freudenthal compactification of the underlying multigraph of the digraph.

中文翻译：

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无限有向图的Edmonds分支定理的类似物

我们将Edmonds的分支定理扩展到局部有限无穷图。如Oxley或Aharoni和Thomassen的示例所示，这无法使用普通的树状结构（其底层图形为树）来完成。相反，我们引入了伪树状概念，并证明了相应的打包结果。最后，我们验证了这些对象的某些树状属性，但还给出了一个示例，即它们的基础图通常不对应于有向图的基础多图的弗洛伊德哈尔紧缩中的拓扑树。