Universal 3-dimensional visibility representations for graphs

Computational Geometry: Theory and Applications

Volumn 9, Issue 1-2, 1998, Pages 111-125

  Alt, Helmut ^a   Godau, Michael ^a   Whitesides, Sue ^b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Geometric graph theory; Graph drawing; Graph representation; Visibility

Indexed keywords

EID: 0012870896     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-7721(97)00015-1     Document Type: Article

References (14)

1. N. Alon, The number of polytopes, configurations and real matroids, Mathematica 33 (1986) 62-71.
2. H. Alt, M. Godau, S. Whitesides, Universal 3-dimensional visibility representations for graphs, in: Proceedings Symposium on Graph Drawing, Passau, Germany, 1995, Lecture Notes in Computer Science 1027, Springer, Berlin, 1995, pp. 8-19.
3. P. Bose, H. Everett, S. Fekete, A. Lubiw, H. Meijer, K. Romanik, T. Shermer, S. Whitesides, On a visibility representation for graphs in three dimensions, in: D. Avis and P. Bose (Eds.), Snapshots of Computational and Discrete Geometry, Vol. 3, McGill University School of Computer Science Technical Report SOCS-94.50, July 1994, pp. 2-25.
4. A. Dean, J. Hutchinson, Rectangle-visibility representations of bipartite graphs, in: Proceedings Graph Drawing, Princeton, NJ, 1994, Lecture Notes in Computer Science 894, Springer, Berlin, 1995, pp. 159-166.
5. G. Di Battista, P. Eades, R. Tamassia, I.G. Tollis, Algorithms for drawing graphs: an annotated bibliography, Computational Geometry: Theory and Applications 4 (5) (1994) 235-282. Also available from wilma.cs.brown.edu by ftp.
6. P. Erdös, G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1935) 463-470.
7. S. Fekete, M. Houle, S. Whitesides, New results on a visibility representation of graphs in 3D, in: Proceedings Symposium on Graph Drawing, Passau, Germany, 1995, Lecture Notes in Computer Science 1027, Springer, Berlin, 1995, pp. 234-241.
8. S. Felsner, Personal communication, 1995.
9. B. Grünbaum, On a conjecture of H. Hadwiger, Pacific J. Math. 11 (1961) 215-219.
10. H. Hadwiger, Über Treffanzahlen bei translationsgleichen Eikörpern, Arch. Math. VIII (1957) 212-213.
11. E. Kranakis, D. Krizanc, J. Urrutia, On the number of directions in visibility representations of graphs, in: Proceedings Graph Drawing, Princeton, NJ, 1994, Lecture Notes in Computer Science 894, Springer, Berlin, 1995, pp. 167-176.
12. K. Romanik, Directed VR-representable graphs have unbounded dimension, in: Proceedings Graph Drawing, Princeton, NJ, 1994, Lecture Notes in Computer Science 894, Springer, Berlin, 1995, pp. 177-181.
13. R. Tamassia, I. Tollis, A unified approach to visibility representations of planar graphs, Discrete Comput. Geom. 1 (1986) 321-341.
14. S. Wismath, Characterizing bar line-of-sight graphs, in: Proceedings ACM Symp. on Computational Geometry, 1985, pp. 147-152.