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DOI: 10.4230/LIPIcs.ISAAC.2021.16
URN: urn:nbn:de:0030-drops-154492
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15449/
Barr, Sam ; Biedl, Therese
Efficiently Partitioning the Edges of a 1-Planar Graph into a Planar Graph and a Forest
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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.
BibTeX - Entry
@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.dagstuhl.de/opus/volltexte/2021/15449},
URN = {urn:nbn:de:0030-drops-154492},
doi = {10.4230/LIPIcs.ISAAC.2021.16},
annote = {Keywords: 1-planar graphs, edge partitions, algorithms, data structures}
}
| Keywords: | 1-planar graphs, edge partitions, algorithms, data structures | |
| Seminar: | 32nd International Symposium on Algorithms and Computation (ISAAC 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 30.11.2021 |
