Cutting up graphs

Combinatorica volume 2, pages15–23(1982)Cite this article

Abstract

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.

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Affiliations

  1. University of Sussex, BN1 9QH, Brighton, U.K.

    M. J. Dunwoody

Authors
  1. M. J. Dunwoody
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Dunwoody, M.J. Cutting up graphs. Combinatorica 2, 15–23 (1982). https://doi.org/10.1007/BF02579278

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AMS subject classification (1980)

  • 05 C 25
  • 20 F 05