Cutting up graphs
- M. J. Dunwoody
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LetΓ be infinite connected graph with more than one end. It is shown that there is a subsetd ⊂V Γ which has the following properties. (i) Bothd andd*=VΓ\d are infinite. (ii) there are only finitely many edges joiningd andd*. (iii) For eachgε AutΓ at least one ofd⊂dg, d*⊂dg, d⊂d* g, d*⊂d* g holds. Any group acting on Γ has a decomposition as a free product with amalgamation or as an HNN-group.
- M. G. Brin, Splitting manifold covering spaces,Preprint, State University of New York, Binghampton.
- W. Dicks,Groups, trees and projective modules, Lecture Notes in Mathematics790, Springer, Berlin-Heidelberg-New York 1980.
- M. J. Dunwoody, Accessibility and groups of cohomological dimension one,Proc. London Math. Soc. 38 (1979) 193–215. CrossRef
- H. D. Macpherson, Infinite distance transitive graphs of finite valency,Combinatorica 2 (1) (1982) 63–69.
- J. R. Stallings,Group theory and three-dimensional manifolds, Yale Mathematical Monographs4 (Yale University Press, 1971).
- L. Babai andM. E. Watkins, Connectivity of infinite graphs having a transitive torsion group action,Arch. Math. 34 (1980), 90–96. CrossRef
- H. A. Jung, A note on fragments of infinite graphs,Combinatorica 1 (1981), 285–288.
- Cutting up graphs
Volume 2, Issue 1 , pp 15-23
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- M. J. Dunwoody (1)
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- 1. University of Sussex, BN1 9QH, Brighton, U.K.