On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs
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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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- On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs
- Book Title
- STACS 98
- Book Subtitle
- 15th Annual Symposium on Theoretical Aspects of Computer Science Paris, France, February 25–27, 1998 Proceedings
- pp 276-286
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- Series Title
- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- Springer-Verlag Berlin Heidelberg
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- Author Affiliations
- 1. Université Paris-Sud, LRI, bât.490, F-91405, Orsay, France
- 2. CNRS, URA 410, Université Paris-Sud, LRI, F-91405, Orsay, France
- 3. Computer and Automation Institute, Hungarian Academy of Sciences, Kende u.13-17, H-1111, Budapest, Hungary
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