Algorithms for some intersection graphs

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


Several intersection graphs such as curves-in-the-plane graphs, circular-arc graphs, chordal graphs and interval graphs are reviewed, especially on their recognition algorithms. In this connection graph realization problem is mentioned.


  1. [1]
    F. Harary, Graph theory, Addison-Wesley, Reading Massachusetts (1972).Google Scholar
  2. [2]
    D.J. Rose, Triangulated graphs and the elimination process, J. Math. Anal. Appl., 32, 597–609 (1970).Google Scholar
  3. [3]
    T. Ohtsuki, H. Mori, E.S. Kuh, T. Kashiwabara and T. Fujisawa, One-dimensional gate assignment and interval graphs, IEEE tran. on CAS Vol. CAS-26, No.9, 675–684 (1979).Google Scholar
  4. [4]
    G. Ehrlich, S. Even and R.E. Tarjan, Intersection graphs of curves in the plane, J. Combinatorial theory (B), 21, 8–20 (1976).Google Scholar
  5. [5]
    S. Even and A. Itai, Queues, stacks and graphs, Theory of machines and computations, Z. Kohavi and A. Paz, ed., Academic Press, New York, 71–86 (1971).Google Scholar
  6. [6]
    M.R. Garey and D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness, H. Freeman and Sons, San Francisco (1978).Google Scholar
  7. [7]
    F. Gavril, Algorithms for a maximum clique and a maximum independent set of a circle graph, Network, 3, 261–273 (1973).Google Scholar
  8. [8]
    A. Tucker, An efficient test for circular-arc graphs, SIAM J. Comput., Vol.9, No.1, 1–24 (1980).Google Scholar
  9. [9]
    F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, J. Combinatorial theory (B), 16, 47–56 (1974).Google Scholar
  10. [10]
    D.J. Rose, R.E. Tarjan and G.S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., Vol.5, No.2, 266–283 (1976).Google Scholar
  11. [11]
    F. Gavril, Algorithms for minimum coloring, maximum clique, minimum covering by cliques and maximum independent set of a chordal graph, SIAM J. Comput., 1, 180–187 (1972).Google Scholar
  12. [12]
    T. Oyamada and T. Ohtsuki, Interval graphs and layout design of MOS arrays, IECE technical report CST75–83 (1975) (in Japanese).Google Scholar
  13. [13]
    T. Yoshida, An algorithm for obtaining a perfect order of an interval graph, monograph, Osaka University (1976) (in Japanese).Google Scholar
  14. [14]
    K.S. Booth and G.S. Lueker, Testing for the consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms J. Computer and System Sciences, 13, 335–379 (1976).Google Scholar
  15. [15]
    S. Fujishige, An efficient algorithm for solving the graph-realization problem by means of PQ-trees, Proceedings of 1979 ISCAS, IEEE catalog No. 79 CH 1421-7 CAS. 1012–1015 (1979).Google Scholar
  16. [16]
    S. Fujishige, An efficient algorithm for solving the graph-realization problem, IECE technical report CST78-136 (1979) (in Japanese).Google Scholar
  17. [17]
    A. Lempel, S. Even and I. Cederbaum, An algorithm for planarity testing of graphs, in "Theory of graphs: international Symposium: Rome, July, 1966" (P. Rosenstiehl, Ed.), 215–232, Gordon and Breach, New York (1967).Google Scholar
  18. [18]
    K.S. Booth, PQ-tree algorithms, Ph.D. Dissertation, Department of Electrical Engineering and Computer Sciences, University of California Berkeley, California (1975).Google Scholar
  19. [19]
    T. Kashiwabara and T. Fujisawa, An NP-complete problem on interval graph, Proceedings of 1979 ISCAS, 82–83 (1979).Google Scholar
  20. [20]
    T. Kashiwabara, Y. Masaki and T. Fujisawa, Complexity of inter-valization of graphs, IECE technical report CST77-15 (1977) (in Japanese).Google Scholar
  21. [21]
    G.S. Lueker, Efficient algorithms for chordal graphs and interval graphs, Ph.D. Dissertation, Program in Applied Mathematics and the Department of Electrical Engineering, Princeton University, Princeton N.J., (1975).Google Scholar
  22. [22]
    C.G. Lekkerkerker and J. Ch. Boland, Representation of a finite graph by a set of intervals on the real line, Fundamenta Mathematicae, 51, 45–64 (1962).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • T. Kashiwabara
    • 1
  1. 1.Dept. of Information and Computer Sciences Faculty of Engineering ScienceOsaka UniversityToyonakaJapan

Personalised recommendations