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

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Abstract

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.

Original languageEnglish
Title of host publicationGraph Drawing - 8th International Symposium, GD 2000 ColonialWilliamsburg, VA, USA, September 20-23, 2000 Proceedings
PublisherSpringer-Verlag London Ltd.
Pages259-271
Number of pages13
ISBN (Print)3540415548, 9783540415541
DOIs
Publication statusPublished - 1 Jan 2001
Externally publishedYes
EventGraph Drawing 2000 - Colonial Williamsburg, United States of America
Duration: 20 Sep 200023 Sep 2000
Conference number: 8th
https://link.springer.com/book/10.1007/3-540-44541-2 (Proceedings)

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1984
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceGraph Drawing 2000
Abbreviated titleGD 2000
CountryUnited States of America
CityColonial Williamsburg
Period20/09/0023/09/00
Internet address

Cite this

Wood, D. R. (2001). Lower bounds for the number of bends in three-dimensional orthogonal graph drawings. In Graph Drawing - 8th International Symposium, GD 2000 ColonialWilliamsburg, VA, USA, September 20-23, 2000 Proceedings (pp. 259-271). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1984). Springer-Verlag London Ltd.. https://doi.org/10.1007/3-540-44541-2_25