Jonathan L. Gross ; Michal Kotrbčík ; Timothy Sun - Genus distributions of cubic series-parallel graphs

dmtcs:2099 - Discrete Mathematics & Theoretical Computer Science, August 1, 2014, Vol. 16 no. 3 - https://doi.org/10.46298/dmtcs.2099
Genus distributions of cubic series-parallel graphs

Authors: Jonathan L. Gross ; Michal Kotrbčík ; Timothy Sun

    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.


    Volume: Vol. 16 no. 3
    Section: Graph Theory
    Published on: August 1, 2014
    Submitted on: May 10, 2012
    Keywords: graph embedding,genus distribution,series-parallel graphs,bounded treewidth,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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