On the Complexity of the Planar Slope Number Problem

The planar slope number of a planar graph G is defined as the minimum number of slopes that is required for a crossing-free straight-line drawing of G. We show that determining the planar slope number is hard in the existential theory of the reals. We discuss consequences for drawings that minimize the planar slope number. Submitted: October 2016 Reviewed: December 2016 Revised: January 2017 Accepted: January 2017 Final: January 2017 Published: January 2017 Article type: Concise paper Communicated by: G. Liotta The results in this paper are part of the authors dissertation at TU Berlin [11], supported by the Deutsche Forschungsgemeinschaft within the research training group ’Methods for Discrete Structure’ (GRK 1408). The results were presented at the Canadian Conference on Computational Geometry 2016. E-mail address: [email protected] (Udo Hoffmann) 184 Udo Hoffmann On the Complexity of the Planar Slope Number Problem