Embedding Four-Directional Paths on Convex Point Sets

A directed path whose edges are assigned labels “up”, “down”, “right”, or “left” is called four-directional, and three-directional if at most three out of the four labels are used. A direction-consistent embedding of an n-vertex threeor four-directional path P on a set S of n points in the plane is a straight-line drawing of P where each vertex of P is mapped to a distinct point of S and every edge points to the direction specified by its label. We study planar direction-consistent embeddings of threeand four-directional paths and provide a complete picture of the problem for convex point sets. Submitted: October 2014 Accepted: August 2015 Final: September 2015 Published: Article type: Regular paper Communicated by: C. Duncan and A. Symvonis O.A. supported by the ESF EUROCORES programme EuroGIGA ComPoSe, Austrian Science Fund (FWF): I 648-N18. T.H. supported by the Austrian Science Fund (FWF): P23629-N18 ‘Combinatorial Problems on Geometric Graphs’. E-mail addresses: [email protected] (Oswin Aichholzer) [email protected] (Thomas Hackl) [email protected] (Sarah Lutteropp) [email protected] (Tamara Mchedlidze) [email protected] (Birgit Vogtenhuber) JGAA, 0(0) 0–0 (0) 1