  We investigate the complexity of finding a transformation from a given
spanning tree in a graph to another given spanning tree in the same graph via a
sequence of edge flips. The exchange property of the matroid bases immediately
yields that such a transformation always exists if we have no constraints on
spanning trees. In this paper, we wish to find a transformation which passes
through only spanning trees satisfying some constraint. Our focus is bounding
either the maximum degree or the diameter of spanning trees, and we give the
following results. The problem with a lower bound on maximum degree is solvable
in polynomial time, while the problem with an upper bound on maximum degree is
PSPACE-complete. The problem with a lower bound on diameter is NP-hard, while
the problem with an upper bound on diameter is solvable in polynomial time.
