Inverse HAMILTONIAN CYCLE and Inverse 3-D MATCHING Are coNP-Complete

  • Michael Krüger
  • Harald Hempel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


In this paper we show that the inverse problems of HAMILTONIAN CYCLE and 3-D MATCHING are coNP complete. This completes the study of inverse problems of the six natural NP-complete problems from [2] and answers an open question from [1]. We classify the inverse complexity of the natural verifier for HAMILTONIAN CYCLE and 3-D MATCHING by showing coNP-completeness of the corresponding inverse problems.


computational complexity coNP-completeness inverse NP-problems HAMILTONIAN CYCLE 3-DIMENSIONAL MATCHING 


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  1. 1.
    Chen, H.: Inverse NP problems. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 338–347. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, New York (1979)zbMATHGoogle Scholar
  3. 3.
    Hemaspaandra, E.L., Hempel, H.: All superlinear inverse schemes are coNP-hard. Theoretical Computer Science 345(2-3), 345–358 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kavvadias, D., Sideri, M.: The inverse satisfiability problem. SIAM Journal on Computing 28(1), 152–163 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)zbMATHGoogle Scholar
  6. 6.
    West, D.B.: Introduction to Graph Theory. Prentice-Hall, Englewood Cliffs (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michael Krüger
    • 1
  • Harald Hempel
    • 1
  1. 1.Institut für InformatikFriedrich-Schiller-Universität Jena 

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