### Genus distributions of cubic series-parallel graphs

*Jonathan L. Gross, Michal Kotrbčík, Timothy Sun*

#### Abstract

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.

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