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DOI: 10.7155/jgaa.00095
ThreeDimensional 1Bend Graph Drawings
Vol. 8, no. 3, pp. 357366, 2004. Concise paper.
Abstract We consider threedimensional griddrawings 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
threedimensional griddrawing with O(n^{3}/log^{2}
n) volume and one bend per edge. The best previous bound was O(n^{3}).
