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

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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.

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Authors and Affiliations

  1. Department of Computer Science, National Chiao Tung University, Hsinchu, 30050, Taiwan

    Tz-Liang Kueng, Cheng-Kuan Lin, Tyne Liang & Jimmy J. M. Tan

  2. Department of Computer Science and Information Engineering, Providence University, Taichung, 43301, Taiwan

    Lih-Hsing Hsu

Authors
  1. Tz-Liang Kueng
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  2. Cheng-Kuan Lin
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  3. Tyne Liang
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  4. Jimmy J. M. Tan
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  5. Lih-Hsing Hsu
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Corresponding author

Correspondence to Tyne Liang.

Additional information

This work was supported in part by the National Science Council of the Republic of China under Contract NSC 95-2221-E-233-002.

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Kueng, TL., Lin, CK., Liang, T. et al. A note on fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges. J Comb Optim 17, 312–322 (2009). https://doi.org/10.1007/s10878-007-9113-1

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  • DOI: https://doi.org/10.1007/s10878-007-9113-1

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