On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs
 Cristina Bazgan,
 Miklos Santha,
 Zsolt Tuza
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Abstract
It is a simple fact that cubic Hamiltonian graphs have at least two Hamiltonian cycles. Finding such a cycle is NPhard 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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 Title
 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
 Pages
 pp 276286
 Copyright
 1998
 DOI
 10.1007/BFb0028567
 Print ISBN
 9783540642305
 Online ISBN
 9783540697053
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1373
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
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 Editors
 Authors

 Cristina Bazgan ^{(1)}
 Miklos Santha ^{(2)}
 Zsolt Tuza ^{(3)}
 Author Affiliations

 1. Université ParisSud, LRI, bât.490, F91405, Orsay, France
 2. CNRS, URA 410, Université ParisSud, LRI, F91405, Orsay, France
 3. Computer and Automation Institute, Hungarian Academy of Sciences, Kende u.1317, H1111, Budapest, Hungary
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