On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs

  • Cristina Bazgan
  • Miklos Santha
  • Zsolt Tuza
Algorithms and Data Structures III

DOI: 10.1007/BFb0028567

Volume 1373 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Bazgan C., Santha M., Tuza Z. (1998) On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs. In: Morvan M., Meinel C., Krob D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg

Abstract

It is a simple fact that cubic Hamiltonian graphs have at least two Hamiltonian cycles. Finding such a cycle is NP-hard in general, and no polynomial time algorithm is known for the problem of fording a second Hamiltonian cycle when one such cycle is given as part of the input. We investigate the complexity of approximating this problem where by a feasible solution we mean a(nother) cycle in the graph. First we prove a negative result showing that the LONGEST PATH problem is not constant approximable in cubic Hamiltonian graphs unless P = NP. No such negative result was previously known for this problem in Hamiltonian graphs. In strong opposition with this result we show that there is a polynomial time approximation scheme for fording another cycle in cubic Hamiltonian graphs if a Hamiltonian cycle is given in the input.

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Cristina Bazgan
    • 1
  • Miklos Santha
    • 2
  • Zsolt Tuza
    • 3
  1. 1.Université Paris-Sud, LRIOrsayFrance
  2. 2.CNRS, URA 410, Université Paris-Sud, LRIOrsayFrance
  3. 3.Computer and Automation Institute, Hungarian Academy of SciencesBudapestHungary