Properties and Complexity of Fan-Planarity
arXiv:1406.5299 · doi:10.1016/j.tcs.2015.04.020
Abstract
In a \emph{fan-planar drawing} of a graph an edge can cross only edges with a common end-vertex. Fan-planar drawings have been recently introduced by Kaufmann and Ueckerdt, who proved that every -vertex fan-planar drawing has at most edges, and that this bound is tight for . We extend their result, both from the combinatorial and the algorithmic point of view. We prove tight bounds on the density of constrained versions of fan-planar drawings and study the relationship between fan-planarity and -planarity. Furthermore, we prove that deciding whether a graph admits a fan-planar drawing in the variable embedding setting is NP-complete.