Article

Combinatorica

, Volume 2, Issue 1, pp 15-23

First online:

Cutting up graphs

  • M. J. DunwoodyAffiliated withUniversity of Sussex

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Abstract

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.

AMS subject classification (1980)

05 C 25 20 F 05