2001 | OriginalPaper | Buchkapitel
Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
verfasst von : David R. Wood
Erschienen in: Graph Drawing
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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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.