On rectangle visibility graphs

  • Prosenjit Bose
  • Alice Dean
  • Joan Hutchinson
  • Thomas Shermer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1190)


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. 1.

    For 1 ≤ k ≤ 4, k-trees are RVGs.

  2. 2.

    Any graph that can be decomposed into two caterpillar forests is an RVG.

  3. 3.

    Any graph whose vertices of degree four or more form a distance-two independent set is an RVG.

  4. 4.

    Any graph with maximum degree four is an RVG. Our proofs are constructive and yield linear-time layout algorithms.



  1. 1.
    T. Biedl. personal communication, 1995.Google Scholar
  2. 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. 3.
    A. M. Dean and J. P. Hutchinson. Combinatorial representations of visibility graphs. preprint, 1996.Google Scholar
  4. 4.
    A. M. Dean and J. P. Hutchinson. Rectangle-visibility representations of bipartite graphs. Discrete Applied Mathematics, 1996, to appear.Google Scholar
  5. 5.
    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.CrossRefGoogle Scholar
  6. 6.
    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.CrossRefGoogle Scholar
  7. 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. 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
  9. 9.
    F. Luccio, S. Mazzone, and C. K. Wong. A note on visibility graphs. Discrete Mathematics, 64:209–219, 1987.CrossRefGoogle Scholar
  10. 10.
    T. C. Shermer. On rectangle visibility graphs II. k-hilly and maximum-degree 4. manuscript, 1996.Google Scholar
  11. 11.
    T. C. Shermer. On rectangle visibility graphs III. external visibility and complexity. manuscript, 1996.Google Scholar
  12. 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. 13.
    S. K. Wismath. Characterizing bar line-of-sight graphs. In Proc. 1st Symp. Comp. Geom., pages 147–152. ACM, 1985.Google Scholar
  14. 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

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Alice Dean
    • 2
  • Joan Hutchinson
    • 3
  • Thomas Shermer
    • 4
  1. 1.Université du Québec à Trois-RivièresCanada
  2. 2.Skidmore CollegeUSA
  3. 3.Macalester CollegeUSA
  4. 4.Simon Fraser UniversityCanada

Personalised recommendations