Monotone drawings of planar graphs

Janos Pach, Geza Toth

Published 2011-01-05Version 1

Let G be a graph drawn in the plane so that its edges are represented by x-monotone curves, any pair of which cross an even number of times. We show that G can be redrawn in such a way that the x-coordinates of the vertices remain unchanged and the edges become non-crossing straight-line segments.