Genus distributions of cubic series-parallel graphs

Jonathan L. Gross (1) , Michal Kotrbčík (2) , Timothy Sun (1)

1 Department of Computer Science [New York]
2 ICS / MUNI - Institute of Computer Science [Brno]

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.

Mots clés: graph embedding; genus distribution; series-parallel graphs; bounded treewidth

Domaines: Mathématique discrète [cs.DM]

Jonathan L. Gross, Michal Kotrbčík, Timothy Sun. Genus distributions of cubic series-parallel graphs. Discrete Mathematics and Theoretical Computer Science, 2014, Vol. 16 no. 3 (3), pp.129--146. ⟨10.46298/dmtcs.2099⟩. ⟨hal-01188913⟩