We give a new characterisation of virtually free groups using graph minors. Namely, we prove that a finitely generated, infinite group is virtually free if and only if for any finite generating set, the corresponding Cayley graph is minor excluded. This answers a question of Ostrovskii and Rosenthal. The proof relies on showing that a finitely generated group that is minor excluded with respect to every finite generating set is accessible, using a graph-theoretic characterisation of accessibility due to Thomassen and Woess.

中文翻译：

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通过次要排除对几乎自由群体的表征

我们使用图未成年人对几乎自由的群体进行了新的表征。也就是说，我们证明了一个有限生成的无限群实际上是自由的，当且仅当对于任何有限生成集，相应的凯莱图被轻微排除。这回答了 Ostrovskii 和 Rosenthal 的问题。证明依赖于显示一个有限生成的群，该群相对于每个有限生成集被次要排除，使用由于 Thomassen 和 Woess 的可访问性的图论表征。