Abstract. In the introductory talk Manuel Urbina Moreano will show how to find an automorphism invariant tree decomposition of graphs with arbitrary finite connectivity. This generalizes Tutte's decomposition of 2-connected graphs.

Bernhard Krön will then explain how this fits into the axiomatic theory of vertex cuts. Another main application concerns groups with more than one end and splittings over finite subgroups (Bass-Serre Theory, Stalling's Theorem on groups with more than one end).

M.J. Dunwoody, B. Krön, Vertex Cuts, to appear in Proc. London Math. Soc.