Genus Distributions of cubic series-parallel graphs

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 y...

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Bibliographic Details
Main Authors Gross, Jonathan L, Kotrbčík, Michal, Sun, Timothy
Format Journal Article
LanguageEnglish
Published 30.07.2014
Subjects
Computer Science - Discrete Mathematics
Mathematics - Combinatorics
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Summary: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.
DOI:10.48550/arxiv.1407.8031