Parameterized Complexity of 1-Planarity
Data Structures and Algorithms
2018-12-18 v1
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.
Cite
@article{arxiv.1304.5591,
title = {Parameterized Complexity of 1-Planarity},
author = {Michael J. Bannister and Sergio Cabello and David Eppstein},
journal= {arXiv preprint arXiv:1304.5591},
year = {2018}
}
Comments
WADS 2013