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arXiv · 0905.0064

Vertex Cuts

M. J. Dunwoody·B. Krön
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Abstract

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.

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M. J. Dunwoody, B. Krön. 2009-05-01. Vertex Cuts. https://arxiv.org/abs/0905.0064

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