Parameterized complexity of 1-planarity

Authors:
Michael J. Bannister;Sergio Cabello;David Eppstein
Affiliations:
Department of Computer Science, University of California, Irvine;Faculty of Mathematics and Physics, University of Ljubljana, Slovenia;Department of Computer Science, University of California, Irvine
Venue:
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Year:
2013

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Abstract

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.