On rectangle visibility graphs
For 1 ≤ k ≤ 4, k-trees are RVGs.
Any graph that can be decomposed into two caterpillar forests is an RVG.
Any graph whose vertices of degree four or more form a distance-two independent set is an RVG.
Any graph with maximum degree four is an RVG. Our proofs are constructive and yield linear-time layout algorithms.
- 1.T. Biedl. personal communication, 1995.Google Scholar
- 2.P. Bose, A. Dean, J. Hutchinson, and T. Shermer. On rectangle visibility graphs I. k-trees and caterpillar forests. manuscript, 1996.Google Scholar
- 3.A. M. Dean and J. P. Hutchinson. Combinatorial representations of visibility graphs. preprint, 1996.Google Scholar
- 4.A. M. Dean and J. P. Hutchinson. Rectangle-visibility representations of bipartite graphs. Discrete Applied Mathematics, 1996, to appear.Google Scholar
- 7.P. Horak and L. Niepel. A short proof of a linear arboricity theorem for cubic graphs. Acta Math. Univ. Comenian., XL-XLI:255–277, 1982.Google Scholar
- 8.J. P. Hutchinson, T. Shermer, and A. Vince. On representations of some thickness-two graphs (extended abstract). In F. Brandenburg, editor, Proc. of Workshop on Graph Drawing, volume 1027 of Lecture Notes in Computer Science. Springer-Verlag, 1995.Google Scholar
- 10.T. C. Shermer. On rectangle visibility graphs II. k-hilly and maximum-degree 4. manuscript, 1996.Google Scholar
- 11.T. C. Shermer. On rectangle visibility graphs III. external visibility and complexity. manuscript, 1996.Google Scholar
- 12.R. Tamassia and I.G. Tollis. A unified approach to visibility representations of planar graphs. Discrete and Computational Geometry, 1:321–341, 1986.Google Scholar
- 13.S. K. Wismath. Characterizing bar line-of-sight graphs. In Proc. 1st Symp. Comp. Geom., pages 147–152. ACM, 1985.Google Scholar
- 14.S. K. Wismath. Bar-Representable Visibility Graphs and a Related Network Flow Problem. PhD thesis, Department of Computer Science, University of British Columbia, 1989.Google Scholar