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DOI: 10.4230/LIPIcs.ISAAC.2021.16
Efficiently Partitioning the Edges of a 1-Planar Graph into a Planar Graph and a Forest

Authors: Sam Barr and Therese Biedl

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
1-planar graphs are graphs that can be drawn in the plane such that any edge intersects with at most one other edge. Ackerman showed that the edges of a 1-planar graph can be partitioned into a planar graph and a forest, and claims that the proof leads to a linear time algorithm. However, it is not clear how one would obtain such an algorithm from his proof. In this paper, we first reprove Ackerman’s result (in fact, we prove a slightly more general statement) and then show that the split can be found in linear time by using an edge-contraction data structure by Holm, Italiano, Karczmarz, Łącki, Rotenberg and Sankowski.
Cite as

Sam Barr and Therese Biedl. Efficiently Partitioning the Edges of a 1-Planar Graph into a Planar Graph and a Forest. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{barr_et_al:LIPIcs.ISAAC.2021.16,
  author =	{Barr, Sam and Biedl, Therese},
  title =	{{Efficiently Partitioning the Edges of a 1-Planar Graph into a Planar Graph and a Forest}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.16},
  URN =		{urn:nbn:de:0030-drops-154492},
  doi =		{10.4230/LIPIcs.ISAAC.2021.16},
  annote =	{Keywords: 1-planar graphs, edge partitions, algorithms, data structures}
}
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