ABSTRACT
This chapter is concerned with fixed box theorems. We saw that trees have two types of subgraphs that are stabilized by all automorphisms: the center and the distance center. This holds for median graphs in general. Theorem 12.21 states that every median graph (i.e., retract of a hypercube) contains a subcube that is stabilized by all automorphisms. One type of subcube is obtained by successive removal of vertices at the periphery, the other type is the distance center.
