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

Cristina Bazgan, Miklos Santha, Z. Tuza

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages276-286
Number of pages11
Volume1373 LNCS
DOIs
Publication statusPublished - 1998
Event15th Annual Symposium on Theoretical Aspects of Computer Science, STACS 98 - Paris, France
Duration: Feb 25 1998Feb 27 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1373 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other15th Annual Symposium on Theoretical Aspects of Computer Science, STACS 98
CountryFrance
CityParis
Period2/25/982/27/98

Fingerprint

Hamiltonian Graph
Hamiltonians
Cubic Graph
Hamiltonian circuit
Cycle
Approximation
Polynomial Time Approximation Scheme
Polynomial-time Algorithm
Polynomials
NP-complete problem
Graph in graph theory

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bazgan, C., Santha, M., & Tuza, Z. (1998). On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs (extended abstract). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1373 LNCS, pp. 276-286). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1373 LNCS). https://doi.org/10.1007/BFb0028567

On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs (extended abstract). / Bazgan, Cristina; Santha, Miklos; Tuza, Z.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1373 LNCS 1998. p. 276-286 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1373 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bazgan, C, Santha, M & Tuza, Z 1998, On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs (extended abstract). in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1373 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1373 LNCS, pp. 276-286, 15th Annual Symposium on Theoretical Aspects of Computer Science, STACS 98, Paris, France, 2/25/98. https://doi.org/10.1007/BFb0028567
Bazgan C, Santha M, Tuza Z. On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs (extended abstract). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1373 LNCS. 1998. p. 276-286. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/BFb0028567
Bazgan, Cristina ; Santha, Miklos ; Tuza, Z. / On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs (extended abstract). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1373 LNCS 1998. pp. 276-286 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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