Efficiently Partitioning the Edges of a 1-Planar Graph into a Planar Graph and a Forest

Authors Sam Barr, Therese Biedl

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Sam Barr
  • University of Waterloo, Canada
Therese Biedl
  • University of Waterloo, Canada

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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)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Dynamic graph algorithms
  • 1-planar graphs
  • edge partitions
  • algorithms
  • data structures


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