Abstract
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 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 three- and four-directional paths and provide a complete picture of the problem for convex point sets.
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’.
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Aichholzer, O., Hackl, T., Lutteropp, S., Mchedlidze, T., Vogtenhuber, B. (2014). Embedding Four-Directional Paths on Convex Point Sets. In: Duncan, C., Symvonis, A. (eds) Graph Drawing. GD 2014. Lecture Notes in Computer Science, vol 8871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45803-7_30
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