We consider locally finite, connected, quasi-transitive graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This can be seen as a graph-theoretical version of Stallings' splitting theorem for multi-ended finitely generated groups and indeed it implies this theorem. Our result also leads to a characterisation of accessible graphs. We obtain applications of our results for planar graphs (answering a variant of a question by Mohar in the affirmative) and graphs without thick ends.

中文翻译：

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准传递图的一个 Stallings 类型定理

我们考虑局部有限的、连通的、准传递图，并表明每个具有多个端点的此类图都是其他两个此类图的树合并。这可以看作是斯托林斯分裂定理的图论版本，用于多端有限生成群，实际上它暗示了这个定理。我们的结果还导致了可访问图的表征。我们将我们的结果应用于平面图（肯定地回答 Mohar 的问题的变体）和没有粗端的图。