  We introduce in a general setting a dynamic programming method for solving
reconfiguration problems. Our method is based on contracted solution graphs,
which are obtained from solution graphs by performing an appropriate series of
edge contractions that decrease the graph size without losing any critical
information needed to solve the reconfiguration problem under consideration.
Our general framework captures the approach behind known reconfiguration
results of Bonsma (2012) and Hatanaka, Ito and Zhou (2014). As a third example,
we apply the method to the following problem: given two $k$-colorings $\alpha$
and $\beta$ of a graph $G$, can $\alpha$ be modified into $\beta$ by recoloring
one vertex of $G$ at a time, while maintaining a $k$-coloring throughout? This
problem is known to be PSPACE-hard even for bipartite planar graphs and $k=4$.
By applying our method in combination with a thorough exploitation of the graph
structure we obtain a polynomial time algorithm for $(k-2)$-connected chordal
graphs.
