Vertex Cuts
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 -connectivity for any . 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.
Keywords
Cite
@article{arxiv.0905.0064,
title = {Vertex Cuts},
author = {M. J. Dunwoody and B. Krön},
journal= {arXiv preprint arXiv:0905.0064},
year = {2015}
}
Comments
35 pages, 14 figures. 34 pages and 14 figures. The version of TikZ used by arXiv corrupts some of the diagrams in this paper. For uncorrupted diagrams go to http://homepage.univie.ac.at/bernhard.kroen/AMSvert14-1-14.pdf or http://www.personal.soton.ac.uk/mjd7/AMSvert14-1-14.pdf