Lower bounds for planar orthogonal drawings of graphs
Information Processing Letters
The techniques of Komolgorov and Bardzin for three-dimensional orthogonal graph drawings
Information Processing Letters
Three-dimensional orthogonal graph drawing algorithms
Discrete Applied Mathematics
Proceedings of the 6th International Symposium on Graph Drawing
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
3DCube: A Tool for Three Dimensional Graph Drawing
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
A Split&Push Approach to 3D Orthogonal Drawing
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
An Algorithm for Three-Dimensional Orthogonal Graph Drawing
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
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In this paper we present the first non-trivial lower bounds for the total number of bends in 3-D orthogonal drawings of maximum degree six graphs. In particular, we prove lower bounds for the number of bends in 3-D 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 c-connected simple graphs and multigraphs (2 ≤ c ≤ 6) of maximum degree Δ (3 ≤ Δ ≤ 6) 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 3-D orthogonal graph drawings. These results have significant ramifications for the '2-bends' problem, which is one of the most important open problems in the field.