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Genus distributions of cubic series-parallel graphs

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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Jonathan L. Gross, Michal Kotrbčík, Timothy Sun. Genus distributions of cubic series-parallel graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (in progress) (3), pp.129--146. ⟨hal-01188913⟩

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