Monotone drawings of planar graphs
Janos Pach, Geza Toth

TL;DR
This paper proves that any planar graph with an x-monotone drawing and even crossings can be redrawn with straight-line edges without crossings, preserving vertex x-coordinates.
Contribution
It introduces a method to convert x-monotone drawings with even crossings into crossing-free straight-line drawings while keeping vertex x-coordinates fixed.
Findings
Any such graph can be redrawn with straight-line edges without crossings
Vertex x-coordinates can be preserved during the redraw
The method applies to graphs with x-monotone edge representations
Abstract
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.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Remote Sensing and LiDAR Applications · 3D Modeling in Geospatial Applications
