Planarity for clustered graphs

  • Qing-Wen Feng
  • Robert F. Cohen
  • Peter Eades
Session 3. Chair: Giuseppe Italiano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 979)


In this paper, we introduce a new graph model known as clustered graphs, i.e. graphs with recursive clustering structures. This graph model has many applications in informational and mathematical sciences. In particular, we study C-planarity of clustered graphs. Given a clustered graph, the C-planarity testing problem is to determine whether the clustered graph can be drawn without edge crossings, or edge-region crossings. In this paper, we present efficient algorithms for testing C-planarity and finding C-planar embeddings of clustered graphs.


Outer Face Classical Graph Simple Closed Curve Representative Graph Planar Embedding 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass., 1974.Google Scholar
  2. 2.
    G. Di Battista, P. Eades, R. Tamassia, and I. Tollis. Algorithms for drawing graphs: An annotated bibliography. Technical report, Department of Computer Science, Brown University, 1993. To appear in Computational Geometry and Applications, currently available from by ftp.Google Scholar
  3. 3.
    Claude Berge. Hypergraphs. North-Holland, 1989.Google Scholar
  4. 4.
    K. Booth and G. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335–379, 1976.Google Scholar
  5. 5.
    N. Chiba, T. Nishizeki, S. Abe, and T. Ozawa. A linear algorithm for embedding planar graphs using PQ-trees. J. of Computer and Sytem Sciences, 30(1):54–76, 1985.CrossRefGoogle Scholar
  6. 6.
    H. de Fraysseix and P. Rosenstiehl. A depth-first-search characterization of planarity. Annals of Discrete Mathematics, 13:75–80, 1982.Google Scholar
  7. 7.
    S. Even and R. E. Tarjan. Computing an st-numbering. Theoretical Computer Science, 2:339–344, 1976.CrossRefGoogle Scholar
  8. 8.
    M.R. Garey and D.S. Johnson. Crossing number is NP-complete. SIAM J. Algebraic and Discrete Methods, 4(3):312–316, 1983.Google Scholar
  9. 9.
    D. Harel. On visual formalisms. Communications of the ACM, 31(5):514–530, 1988.CrossRefGoogle Scholar
  10. 10.
    J. Hopcroft and R. E. Tarjan. Efficient planarity testing. Journal of ACM, 21(4):549–568, 1974.CrossRefGoogle Scholar
  11. 11.
    T. Kamada. Visualizing Abstract Objects and Relations. World Scientific Series in Computer Science, 1989.Google Scholar
  12. 12.
    J. Kawakita. The KJ method — a scientific approach to problem solving. Technical report, Kawakita Research Institute, Tokyo, 1975.Google Scholar
  13. 13.
    Wei Lai. Building Interactive Digram Applications. PhD thesis, Department of Computer Science, University of Newcastle, Callaghan, New South Wales, Australia, 2308, June 1993.Google Scholar
  14. 14.
    A. Lempel, S. Even, and I. Cederbaum. An algorithm for planarity testing of graphs. In Theory of Graphs, International Symposium (Rome 1966), pages 215–232. Gordon and Breach, New York, 1967.Google Scholar
  15. 15.
    T. Nishizeki and N. Chiba. Planar Graphs: Theory and Algorithms, Annals of Discrete Mathematics 32. North-Holland, 1988.Google Scholar
  16. 16.
    S. C. North. Drawing ranked digraphs with recursive clusters. preprint, 1993. Software Systems and Research Center, AT & T Laboratories.Google Scholar
  17. 17.
    K. Sugiyama and K. Misue. Visualization of structural information: Automatic drawing of compound digraphs. IEEE Transactions on Systems, Man and Cybernetics, 21(4):876–892, 1991.Google Scholar
  18. 18.
    C. Williams, J. Rasure, and C. Hansen. The state of the art of visual languages for visualization. In Visualization 92, pages 202–209, 1992.Google Scholar
  19. 19.
    Rebecca Wirfs-Brock, Brian Wilkerson, and Lauren Wiener. Designing Object-Oriented Software. P T R Prentics Hall, Englewood Cliffs, NJ 07632, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Qing-Wen Feng
    • 1
  • Robert F. Cohen
    • 1
  • Peter Eades
    • 1
  1. 1.Department of Computer ScienceUniversity of NewcastleCallaghanAustralia

Personalised recommendations