  We consider combinatorial problems that can be solved in polynomial time for
graphs of bounded treewidth but where the order of the polynomial that bounds
the running time is expected to depend on the treewidth bound. First we review
some recent results for problems regarding list and equitable colorings,
general factors, and generalized satisfiability. Second we establish a new
hardness result for the problem of minimizing the maximum weighted outdegree
for orientations of edge-weighted graphs of bounded treewidth.
