  We derive a quadratic-time algorithm for the genus distribution of any
3-regular, biconnected series-parallel graph, which we extend to any
biconnected series-parallel graph of maximum degree at most 3. Since the
biconnected components of every graph of treewidth 2 are series-parallel
graphs, this yields, by use of bar-amalgamation, a quadratic-time algorithm for
every graph of treewidth at most 2 and maximum degree at most 3.
