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An efficient algorithm to find a Hamiltonian circuit in a 4-connected maximal planar graph

  • T. Asano
  • S. Kikuchi
  • N. Saito
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 108)

Abstract

This paper describes an efficient algorithm to find a Hamiltonian circuit in an arbitrary 4-connected maximal planar graph. The algorithm is based on our simlplified version of Whitney's proof of his theorem: every 4-connected maximal planar graph has a Hamiltonian circuit.

References

  1. [1]
    A. V. Aho, J. E. Hoperoft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass., 1974.Google Scholar
  2. [2]
    R. E. Bixby and D. Wang, An algorithm for finding hamiltonian circuits in certain graphs, Mathematical Programming Study, 8(1978), pp. 35–49.Google Scholar
  3. [3]
    J. A. Bondy and V. Chvátal, A method in graph theory, Discrete Math., 15(1976), pp. 111–135.Google Scholar
  4. [4]
    M. R. Garey, D. S. Johnson and R. E. Tarjan, The planar Hamiltonian circuit problem is NP-complete, SIAM J. Comput., 5(1976), pp. 704–714.Google Scholar
  5. [5]
    D. Gouyou-Beauchamps, Un algorithme de recherche de circuit Hamiltonien dans les graphes 4-connexes planaries, Colloques Internationaux CNRS, No. 260 — Probléms Combinatoires et Theorie des Graphes, ed, J.C. Bermond, J.C. Fournier, M. Las Vergnas and D. Scotteau, (1978), pp. 185–187.Google Scholar
  6. [6]
    F. Harary, Graph Theory, Addison-Welsey, Reading, Mass., 1969.Google Scholar
  7. [7]
    J. E. Hopcroft and R. E. Tarjan, Efficient planarity testing, J. Assoc. Comput. Mach., 21(1974), pp. 549–568.Google Scholar
  8. [8]
    R. M. Karp, Reducibility among combinatorial problems, in: R. E. Miller and J. W. Thatcher, eds, Complexity of Computer Computations, Plenum Press, New York, (1972) pp. 85–104.Google Scholar
  9. [9]
    W. T. Tutte, A theorem on planar graphs, Trans. Amer. Math. Soc., 82(1956), pp. 99–116.Google Scholar
  10. [10]
    H. Whitney, A theorem on graphs, Annals Math., 32(1931), pp. 378–390.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • T. Asano
    • 1
  • S. Kikuchi
    • 2
  • N. Saito
    • 2
  1. 1.Deparment of Mathematical Engineering and Instrumentation Physics Faculty of EngineeringUniversity of TokyoBunkyo-ku, TokyoJapan
  2. 2.Department of Electrical Communications Faculty of EngineeringTohoku UniversitySendaiJapan

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