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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Submitted on : Monday, August 31, 2015 - 5:03:51 PM Last modification on : Friday, December 18, 2020 - 7:10:03 PM Long-term archiving on: : Tuesday, December 1, 2015 - 10:44:46 AM
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⟩