In a 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 [35], who proved that every n -vertex fan-planar drawing has at most 5n−10 edges, and that this bound is tight for n≥20. We extend their result from both 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 k-planarity. Also, we prove that testing fan-planarity in the variable embedding setting is NP-complete.
Fan-planarity: Properties and complexity
BINUCCI, Carla;DI GIACOMO, Emilio;DIDIMO, WALTER;MONTECCHIANI, FABRIZIO;
2015
Abstract
In a 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 [35], who proved that every n -vertex fan-planar drawing has at most 5n−10 edges, and that this bound is tight for n≥20. We extend their result from both 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 k-planarity. Also, we prove that testing fan-planarity in the variable embedding setting is NP-complete.File in questo prodotto:
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