顶点切割
Vertex Cuts
摘要：
我们推广的结构树理论，这是基于删除100多条边，删除100多个顶点。这给出了Tutte的树分解的2-连通图到3-连通块的一个重要推广。对于有限图，存在一个结构树，该结构树包含关于任何$k$的$k$连通性的信息。该理论也可以应用于具有多于一个顶点端的无限图，即可以通过移除有限数量的顶点来分离的端。这给出了Stallings的结构定理的一个推广的群有一个以上的结束。
英文摘要：
We generalise structure tree theory, which is based on removing finitely many edges, to removing finitely many vertices. This gives a significant generalization of Tutte's tree decomposition of 2-connected graphs into 3-connected blocks. For a finite graph there is a structure tree that contains information about $k$-connectivity for any $k$. The theory can also be applied to infinite graphs that have more than one vertex end, i.e. ends that can be separated by removing a finite number of vertices. This gives a generalization of Stallings' structure theorem for groups with more than one end.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
