Upward numbering testing for triconnected graphs

  • M. Chandramouli
  • A. A. Diwan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1027)

Abstract

In this paper, we look at the problem of upward planar drawings of planar graphs whose vertices have preassigned y-coordinates. We give a linear time algorithm for testing whether such an embedding is feasible for triconnected labelled graphs.

References

  1. 1.
    G. Di Battista and E. Nardelli. An Algorithm for Planarity Testing of Hierarchical Graphs, volume 246 of Lecture Notes in Computer Science, pages 277–289. Springer-Verlag, 1987.Google Scholar
  2. 2.
    G. Di Battista and R. Tamassia. Algorithms for plane representations of acyclic digraphs. Theoretical Computer Science, 61:175–198, 1988.CrossRefGoogle Scholar
  3. 3.
    P. Bertolazzi, G. Di Battista, G. Liotta, and C. Mannino. Upward drawings of triconnected digraphs. Algorithmica, to appear.Google Scholar
  4. 4.
    M. Chandramouli. Upward Planar Graph Drawings. PhD thesis, IIT Bombay, 1994.Google Scholar
  5. 5.
    M. Chandramouli and A. A. Diwan. Intersection graphs of horizontal and vertical line segments in the plane, 1992. Unpublished manuscript.Google Scholar
  6. 6.
    A. Garg and R. Tamassia. On the computational complexity of upward and rectilinear planarity testing. In Graph Drawing 94, DIMACS, 1994.Google Scholar
  7. 7.
    L. S. Heath and S. Pemmaraju. Recognizing leveled-planar dags in linear time. In Proceedings of Graph Drawing '95, 1995.Google Scholar
  8. 8.
    M. D. Hutton and A. Lubiw. Upward planar drawing of single source acyclic digraphs. In Proc. ACM-SIAM Symposium on Discrete Algorithms, pages 203–211, 1991.Google Scholar
  9. 9.
    D. R. Kelly. Fundamentals of planar ordered sets. Discrete Mathematics, 63:197–216, 1987.CrossRefGoogle Scholar
  10. 10.
    J. Kratochvil. A special planar satisfiability problem and some consequences of its np-completeness. Discrete Appl. Math. (to appear).Google Scholar
  11. 11.
    X. Lin. Analysis of Algorithms for Drawing Graphs. PhD thesis, Department of Computer Science, University of Queensland, 1992.Google Scholar
  12. 12.
    R. Tamassia and I. G. Tollis. A unified approach to visibility representations of planar graphs. Disc. and Comp. Geometry, 1(4):321–341, 1986.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • M. Chandramouli
    • 1
  • A. A. Diwan
    • 1
  1. 1.Dept. of Computer Science and EngineeringIndian Institute of TechnologyPowai, BombayIndia

Personalised recommendations