Lower bounds for the number of bends in three-dimensional orthogonal graph drawings

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Abstract

This paper presents the first non-trivial lower bounds for the total number of bends in 3-D orthogonal graph drawings with vertices represented by points. 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, multigraphs, and pseudographs (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.
Original languageEnglish
Pages (from-to)33-77
Number of pages45
JournalJournal of Graph Algorithms and Applications
Volume7
Issue number1
DOIs
Publication statusPublished - 2003
Externally publishedYes

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