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A note on fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges

Author

Listed:
  • Tz-Liang Kueng

    (National Chiao Tung University)

  • Cheng-Kuan Lin

    (National Chiao Tung University)

  • Tyne Liang

    (National Chiao Tung University)

  • Jimmy J. M. Tan

    (National Chiao Tung University)

  • Lih-Hsing Hsu

    (Providence University)

Abstract

In the paper “Fault-free Mutually Independent Hamiltonian Cycles in Hypercubes with Faulty Edges” (J. Comb. Optim. 13:153–162, 2007), the authors claimed that an n-dimensional hypercube can be embedded with (n−1−f)-mutually independent Hamiltonian cycles when f≤n−2 faulty edges may occur accidentally. However, there are two mistakes in their proof. In this paper, we give examples to explain why the proof is deficient. Then we present a correct proof.

Suggested Citation

  • Tz-Liang Kueng & Cheng-Kuan Lin & Tyne Liang & Jimmy J. M. Tan & Lih-Hsing Hsu, 2009. "A note on fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges," Journal of Combinatorial Optimization, Springer, vol. 17(3), pages 312-322, April.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:3:d:10.1007_s10878-007-9113-1
    DOI: 10.1007/s10878-007-9113-1
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    References listed on IDEAS

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    1. Sun-Yuan Hsieh & Pei-Yu Yu, 2007. "Fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 153-162, February.
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