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.

Source : oai:HAL:hal-01188913v1

Volume: Vol. 16 no. 3 (in progress)

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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