Parameterized Complexity of 1-Planarity

  • Michael J. Bannister
  • Sergio Cabello
  • David Eppstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)


We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the parameterized complexity of the problem with respect to the vertex cover number, tree-depth, and cyclomatic number. For these parameters we construct fixed-parameter tractable algorithms. However, the problem remains NP-complete for graphs of bounded bandwidth, pathwidth, or treewidth.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michael J. Bannister
    • 1
  • Sergio Cabello
    • 2
  • David Eppstein
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaIrvineUSA
  2. 2.Faculty of Mathematics and PhysicsUniversity of LjubljanaSlovenia

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