An infinite graph is quasi-transitive if its vertex set has finitely many orbits under the action of its automorphism group. In this paper we obtain a structure theorem for locally finite quasi-transitive graphs avoiding a minor, which is reminiscent of the Robertson-Seymour Graph Minor Structure Theorem. We prove that every locally finite quasi-transitive graph avoiding a minor has a tree-decomposition whose torsos are finite or planar; moreover the tree-decomposition is canonical, i.e. invariant under the action of the automorphism group of . As applications of this result, we prove the following.

中文翻译：

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准传递图的结构避免了次要问题及其在多米诺骨牌问题上的应用


如果无限图的顶点集在其自同构群的作用下具有有限多个轨道，则该图是准传递的。在本文中，我们获得了避免次要的局部有限准传递图的结构定理，这让人想起 Robertson-Seymour 图次要结构定理。我们证明每个避免次要的局部有限准传递图都具有树分解，其躯干是有限的或平面的；此外，树分解是规范的，即在 的自同构群的作用下不变。作为该结果的应用，我们证明以下内容。