标题： 具有应用的粗略Halin网格定理，用于准传递、局部有限图 显示英文标题

标题： A coarse Halin Grid Theorem with applications to quasi-transitive, locally finite graphs

摘要： 我们证明了Halin网格定理的粗略版本：每一个具有一个端点的、局部有限的图，如果其作为渐近子图包含无限多条射线的不相交并集，则它也作为渐近子图包含半网格。 更一般地，我们在对无限射线的子图模型附加必要假设的情况下，证明对于任意（不一定是一个端点或局部有限的）图，同样的结论也成立。 这解决了Georgakopoulos和Papasoglu的猜想。 作为应用，我们证明每个具有一个端点的、准传递的、局部有限的图都作为渐近子图和发散子图包含半网格。 这特别包括所有具有一个端点的有限生成群的局部有限Cayley图，并解决了Georgakopoulos和Papasoglu的问题。 显示英文摘要

摘要： We prove a coarse version of Halin's Grid Theorem: Every one-ended, locally finite graph that contains the disjoint union of infinitely many rays as an asymptotic minor also contains the half-grid as an asymptotic minor. More generally, we show that the same holds for arbitrary (not necessarily one-ended or locally finite) graphs under additional, necessary assumptions on the minor-models of the infinite rays. This resolves a conjecture of Georgakopoulos and Papasoglu. As an application, we show that every one-ended, quasi-transitive, locally finite graph contains the half-grid as an asymptotic minor and as a diverging minor. This in particular includes all locally finite Cayley graphs of one-ended finitely generated groups and solves a problem of Georgakopoulos and Papasoglu.