Cutting up graphs


LetΓ be infinite connected graph with more than one end. It is shown that there is a subsetdV Γ which has the following properties. (i) Bothd andd*=VΓ\d are infinite. (ii) there are only finitely many edges joiningd andd*. (iii) For each AutΓ at least one ofddg, d*⊂dg, dd* 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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Dunwoody, M.J. Cutting up graphs. Combinatorica 2, 15–23 (1982).

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AMS subject classification (1980)

  • 05 C 25
  • 20 F 05