Monotone drawings of planar graphs

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. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 39–47, 2004