Three-dimensional 1-bend graph drawings

@article{Morin2004Threedimensional1G,
  title={Three-dimensional 1-bend graph drawings},
  author={Pat Morin and David R. Wood},
  journal={J. Graph Algorithms Appl.},
  year={2004},
  volume={8},
  pages={357-366}
}
We consider three-dimensional grid-drawings of graphs with at most one bend per edge. Under the additional requirement that the vertices be collinear, we prove that the minimum volume of such a drawing is Θ(cn), where n is the number of vertices and c is the cutwidth of the graph. We then prove that every graph has a three-dimensional grid-drawing with O(n/ log n) volume and one bend per edge. The best previous bound was O(n). 

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