eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-30
16:1
16:15
10.4230/LIPIcs.ISAAC.2021.16
article
Efficiently Partitioning the Edges of a 1-Planar Graph into a Planar Graph and a Forest
Barr, Sam
1
Biedl, Therese
1
University of Waterloo, Canada
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol212-isaac2021/LIPIcs.ISAAC.2021.16/LIPIcs.ISAAC.2021.16.pdf
1-planar graphs
edge partitions
algorithms
data structures