Three-Dimensional 1-Bend Graph Drawings
Vol. 8, no. 3, pp. 357-366, 2004. Concise paper.
Abstract 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(n3/log2 n) volume and one bend per edge. The best previous bound was O(n3).
Submitted: April 2004.
Revised: March 2005.
Communicated by Giuseppe Liotta
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