Reprint of: Upward planar embedding of an n-vertex oriented path on $O(n^2)$ points

Abstract

We prove that every n-vertex oriented path admits an upward planar embedding on every general set of ${(n-1)}^2+1$ points on the plane. This result improves the previously known upper bound which is exponential in the number of switches of the given oriented path (Angelini et al. 2010) [1].