1. Fan-planarity: Properties and complexity.
- Author
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Binucci, Carla, Di Giacomo, Emilio, Didimo, Walter, Montecchiani, Fabrizio, Patrignani, Maurizio, Symvonis, Antonios, and Tollis, Ioannis G.
- Subjects
- *
COMPUTATIONAL complexity , *MATHEMATICAL bounds , *COMBINATORICS , *ALGORITHMS , *MATHEMATICAL proofs - 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 5 n − 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. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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