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

Tz-Liang Kueng; Cheng-Kuan Lin; Tyne Liang; Jimmy J. M. Tan; Lih-Hsing Hsu

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

机译：关于带故障边的超立方体中无故障的相互独立的哈密顿环的一个注记

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摘要

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.

机译：在论文“具有故障边缘的超立方体中的无故障互独立哈密顿环”（J. Comb。Optim。13：153–162，2007）中，作者声称可以将n维超立方体嵌入（n？1当f≤n≤2的故障边缘时，可能会偶然发生相互独立的哈密顿循环。但是，他们的证明有两个错误。在本文中，我们将举例说明为什么证明不足。然后，我们提出正确的证明。

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来源
《Journal of Combinatorial Optimization》 |2009年第3期|312-322|共11页
作者
Tz-Liang Kueng; Cheng-Kuan Lin; Tyne Liang; Jimmy J. M. Tan; Lih-Hsing Hsu;
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作者单位

Department of Computer Science National Chiao Tung University Hsinchu 30050 Taiwan;

Department of Computer Science National Chiao Tung University Hsinchu 30050 Taiwan;

Department of Computer Science National Chiao Tung University Hsinchu 30050 Taiwan;

Department of Computer Science National Chiao Tung University Hsinchu 30050 Taiwan;

Department of Computer Science and Information Engineering Providence University Taichung 43301 Taiwan;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Interconnection network; Hypercube; Fault tolerance; Hamiltonian cycle;

机译：互连网络;超立方体;容错;哈密顿循环;

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专利

1. A note on fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges [J] . Kueng TL, Lin CK, Liang T, Journal of combinatorial optimization . 2009,第3期

机译：关于带故障边的超立方体中无故障的相互独立的哈密顿环的一个注记
2. Fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges [J] . Hsieh SY, Yu PY Journal of combinatorial optimization . 2007,第2期

机译：具有故障边缘的超立方体中的无故障的相互独立的哈密顿循环
3. Fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges [J] . Sun-Yuan Hsieh, Pei-Yu Yu Journal of Combinatorial Optimization . 2007,第2期

机译：具有故障边缘的超立方体中的无故障的相互独立的哈密顿循环
4. Fault-Free Pairwise Independent Hamiltonian Paths on Faulty Hypercubes [C] . Sun-Yuan Hsieh Advances in Computer Systems Architecture; Lecture Notes in Computer Science; 4186 . 2006

机译：故障超立方体上的无故障成对独立哈密顿路径
5. Hamiltonian cycles through specified edges in bipartite graphs, domination game, and the game of revolutionaries and spies. [D] . Nasab, Reza Zamani. 2011

机译：哈密顿量在二部图中的指定边，统治博弈以及革命者和间谍的博弈之间循环。
6. Mutual correction of faulty PCNA subunits in temperature-sensitive lethal mus209 mutants of Drosophila melanogaster. [O] . D S Henderson, U K Wiegand, D G Norman, 2000

机译：对果蝇温度敏感致死性mus209突变体中有缺陷的PCNA亚基进行相互校正。
7. ON THE MUTUALLY INDEPENDENT HAMILTONIAN CYCLES IN FAULTY HYPERCUBES [O] . Preprint Series, Petr Gregor, Riste ˇ Skrekovski 2011

机译：关于断层超高压中的相互独立的哈密顿循环

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

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