Highly Influenced

8 Excerpts

@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} }

- Published in CCCG 2004
DOI:10.7155/jgaa.00095

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).