Journal of Graph Algorithms and Applications
http://jgaa.info ISSN: 1526-1719
DOI: 10.7155/jgaa.00095 Three-Dimensional 1-Bend Graph Drawings Pat Morin and David R. Wood 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 |
Journal of Graph Algorithms and Applications |