Journal of Soviet Mathematics

, Volume 55, Issue 2, pp 1621–1643 | Cite as

The isomorphism problem for classes of graphs closed under contraction

  • I. N. Ponomarenko


We consider the isomorphism problem for graphs in classes which, together with any graph, contain its connected induced subgraphs and graphs obtained by successive identifications of endpoints of edges. The main result is to establish sufficient conditions for the existence of a polynomial time algorithm testing graphs of such classes for isomorphism. It is shown that classes failing to satisfy these conditions are isomorphism-complete.


Endpoint Polynomial Time Time Algorithm Polynomial Time Algorithm Successive Identification 
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Literature cited

  1. 1.
    A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, London (1974).Google Scholar
  2. 2.
    V. P. Zemlyachenko, P. M. Korneenko, and R. I. Tyshkevich, “The graph isomorphism problem,” in: Theory of Computational Complexity, 1 [in Russian], Zap. Nauchn. Seminarov Leningrad. Otd. Mat. Inst. Akad. Nauk SSSR,118, 83–158 (1982).Google Scholar
  3. 3.
    F. Harary, Graph Theory, Addison-Wesley, Reading, Mass. (1969).Google Scholar
  4. 4.
    J. E. Hopcroft and R. E. Tarjan, “Isomorphism of planar graphs,” in: Complexity of Computer Computations, Plenum Press, New York-London (1972), pp. 131–152.Google Scholar
  5. 5.
    L. Babai and E. Luks, “Canonical labeling of graphs,” Proc. 19th Annual ACM Symp. Th. Comput. (1983), pp. 171–183.Google Scholar
  6. 6.
    C. J. Colbourn, “On testing isomorphism of permutation graphs,” Networks,11, 13–21 (1981).Google Scholar
  7. 7.
    M. Furst, J. Hopcroft, and E. Luks, “Polynomial-time algorithms for permutation groups,” in: Proc. 21st Symp. Found. Comput. Sci. (1980), pp. 36–41.Google Scholar
  8. 8.
    I. S. Filotti and J. N. Mayer, “A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus,” in: Proc. 12th Annual ACM Symp. Th. Comput. (1980), pp. 236–243.Google Scholar
  9. 9.
    J. E. Hopcroft and R. M. Karp, “An n5/2 algorithm for maximum matching in bipartite graphs,” SIAM J. Comput.,2, 225–231 (1973).Google Scholar
  10. 10.
    M. Klawe, D. Corneil, and A. Proskurowski, “Isomorphism testing in hook-up classes,” SIAM J. Alg. Discr. Math.,3, 260–274 (1982).Google Scholar
  11. 11.
    D. G. Larman and P. Mani, “On the existence of certain configurations within graphs and 1-skeletons of polytopes,” Proc. London Math. Soc.,20, 144–160 (1970).Google Scholar
  12. 12.
    G. S. Leueker and K. S. Booth, “A linear time algorithm for deciding interval graphs isomorphism,” J. ACM,26, 183–195 (1979).Google Scholar
  13. 13.
    W. Mader, “HomomorphiesÄtze für graphen,” Math. Ann.,178, 154–168 (1968).Google Scholar
  14. 14.
    G. Miller, “Isomorphism testing and canonical forms for k-contractible graphs,” Lect. Notes Comput. Sci.,158, 310–321 (1983).Google Scholar
  15. 15.
    B. Weisfeiler, “On construction and identification of graphs,” Lect. Notes Math.,558 (1976).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • I. N. Ponomarenko

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