Geodesic
Three-Dimensional 1-Bend Graph Drawings
Journal of Graph Algorithms and Applications, Tome 8 (2004) no. 3, pp. 357-366.

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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). 
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     author = {Pat Morin and David Wood},
     title = {Three-Dimensional {1-Bend} {Graph} {Drawings}},
     journal = {Journal of Graph Algorithms and Applications},
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     doi = {10.7155/jgaa.00095},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00095/}
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Pat Morin; David Wood. Three-Dimensional 1-Bend Graph Drawings. Journal of Graph Algorithms and Applications, Tome 8 (2004) no. 3, pp. 357-366. doi : 10.7155/jgaa.00095. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00095/

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