Abstract
We study the problem of drawing a graph in the plane so that the vertices of the graph are rectangles that are aligned with the axes, and the edges of the graph are horizontal or vertical lines-of-sight. Such a drawing is useful, for example, when the vertices of the graph contain information that we wish displayed on the drawing; it is natural to write this information inside the rectangle corresponding to the vertex. We call a graph that can be drawn in this fashion a rectangle-visibility graph, or RVG. Our goal is to find classes of graphs that are RVGs. We obtain several results:
-
1.
For 1 ≤ k ≤ 4, k-trees are RVGs.
-
2.
Any graph that can be decomposed into two caterpillar forests is an RVG.
-
3.
Any graph whose vertices of degree four or more form a distance-two independent set is an RVG.
-
4.
Any graph with maximum degree four is an RVG. Our proofs are constructive and yield linear-time layout algorithms.
Supported by NSERC Canada Reseach Grant OGP0046218, and DIMACS, Rutgers University, funded by NSF under contract STC-91-19999 and the New Jersey Commission on Science and Technology.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
T. Biedl. personal communication, 1995.
P. Bose, A. Dean, J. Hutchinson, and T. Shermer. On rectangle visibility graphs I. k-trees and caterpillar forests. manuscript, 1996.
A. M. Dean and J. P. Hutchinson. Combinatorial representations of visibility graphs. preprint, 1996.
A. M. Dean and J. P. Hutchinson. Rectangle-visibility representations of bipartite graphs. Discrete Applied Mathematics, 1996, to appear.
P. Duchet, Y. Hamidoune, M. Las Vergnas, and H. Meyniel. Representing a planar graph by vertical lines joining different levels. Discrete Mathematics, 46:319–321, 1983.
M. R. Garey, D. S. Johnson, and H. C. So. An application of graph coloring to printed circuit testing. IEEE Transactions on Circuits and Systems, CAS-23:591–599, 1976.
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.
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.
F. Luccio, S. Mazzone, and C. K. Wong. A note on visibility graphs. Discrete Mathematics, 64:209–219, 1987.
T. C. Shermer. On rectangle visibility graphs II. k-hilly and maximum-degree 4. manuscript, 1996.
T. C. Shermer. On rectangle visibility graphs III. external visibility and complexity. manuscript, 1996.
R. Tamassia and I.G. Tollis. A unified approach to visibility representations of planar graphs. Discrete and Computational Geometry, 1:321–341, 1986.
S. K. Wismath. Characterizing bar line-of-sight graphs. In Proc. 1st Symp. Comp. Geom., pages 147–152. ACM, 1985.
S. K. Wismath. Bar-Representable Visibility Graphs and a Related Network Flow Problem. PhD thesis, Department of Computer Science, University of British Columbia, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bose, P., Dean, A., Hutchinson, J., Shermer, T. (1997). On rectangle visibility graphs. In: North, S. (eds) Graph Drawing. GD 1996. Lecture Notes in Computer Science, vol 1190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62495-3_35
Download citation
DOI: https://doi.org/10.1007/3-540-62495-3_35
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62495-0
Online ISBN: 978-3-540-68048-2
eBook Packages: Springer Book Archive