A graph-planarization algorithm and its application to random graphs

  • T. Ozawa
  • H. Takahashi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 108)


In this paper presented are a graph-planarization algorithm and the results obtained by the application of the algorithm to random graphs. The algorithm tests the subgraph of the given graph G for planarity and if the subgraph fails the test, it deletes a minimum number of edges necessary for planarization. The subgraph has one vertex at the beginning, and the number of its vertices is increased one by one until all the vertices of G are included in it. The result from the application of the algorithm to random graphs indicates that the time complexity of the algorithm is O(np) with p=1.4≈1.5 in average, where n is the number of verticles of G.


Random Graph Algorithm Plan Original Graph Interval Graph Delete Edge 
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.


  1. [1]
    Lempel, A., Even, S. and Cederbaum, I. "An algorithm for planarity testing of graphs," Theory of Graphs, International Symposium, Rome, July 1966, Rosenstiel, P. edit., pp. 215–232, Gordon & Breach, N. Y., 1967.Google Scholar
  2. [2]
    Booth, K. S., and Lueker, G. S. "Testing for the consecutive ones property, interval graphs and graph planarity using PQ-trees," J. Computer and Syst. Scie., vol.13, pp. 335–379, 1976.Google Scholar
  3. [3]
    Ozawa, T and Takahashi, H. "An algorithm for planarization of graphs using PQ-trees," Trans. Information Processing Society of Japan, vol. 22, pp. 9–15, 1981; and also Tech. Report, Inst. Electronics and Communication Engineers of Japan, Circuits and Systems, CAS79-150, Jan. 1980.Google Scholar
  4. [4]
    Chiba, T., Nishioka, I. and Shirakawa, I. "An algorithm of maximal planarization of graphs," 1979 International Symposium on Circuits and Systems Proc. pp. 649–653, 1979.Google Scholar
  5. [5]
    Garey, M. and Johnson, D.: "Computers and Intractability," W. H. Freeman and Co., Reading, England, 1979.Google Scholar
  6. [6]
    Ozawa, T. and Nishizeki, T. "Properties of certain types of random graphs," 1979 International Symposium on Circuits and Systems Proc., pp. 88–91, 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • T. Ozawa
    • 1
  • H. Takahashi
    • 1
  1. 1.Department of Electrical Engineering Faculty of EngineeringKyoto UniversityKyotoJapan

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