  For a finitely generated free group F_n, of rank at least 2, any finite
subgroup of Out(F_n) can be realized as a group of automorphisms of a graph
with fundamental group F_n. This result, known as Out(F_n) realization, was
proved by Zimmermann, Culler and Khramtsov. This theorem is comparable to
Nielsen realization as proved by Kerckhoff: for a closed surface with negative
Euler characteristic, any finite subgroup of the mapping class group can be
realized as a group of isometries of a hyperbolic surface. Both of these
theorems have restatements in terms of fixed points of actions on spaces
naturally associated to them. For a nonnegative integer n we define a class of
groups (GVP(n)) and prove a similar statement for their outer automorphism
groups.
