Monotone drawings of planar graphs

János Pach, Géza Tóth
2004 Journal of Graph Theory  
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.
doi:10.1002/jgt.10168 fatcat:2hzsmn4us5h7hcc6x6dwzy6adu