Lower Bounds for the Number of Bends in ThreeDimensional Orthogonal Graph DrawingsWood, David R. (2001) Lower Bounds for the Number of Bends in ThreeDimensional Orthogonal Graph Drawings. In: Graph Drawing 8th International Symposium, GD 2000, September 20–23, 2000 , pp. 259271(Official URL: http://dx.doi.org/10.1007/3540445412_25). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540445412_25
AbstractIn this paper we present the first nontrivial lower bounds for the total number of bends in 3D orthogonal drawings of maximum degree six graphs. In particular, we prove lower bounds for the number of bends in 3D orthogonal drawings of complete simple graphs and multigraphs, which are tight in most cases. These result are used as the basis for the construction of infinite classes of cconnected simple graphs and multigraphs ($2\leq c\leq6$) of maximum degree $\Delta$ ($3\leq\Delta\leq6$) with lower bounds on the total number of bends for all members of the class. We also present lower bounds for the number of bends in general position 3D orthogonal graph drawings. These results have significant ramifications for the `2bends' problem, which is one of the most important open problems in the field.
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