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14. Optimal edge fault-tolerant-prescribed hamiltonian laceability of balanced hypercubes

Author

Song, Ningning and Yang, Yuxing

Subjects
Mathematics - Combinatorics, 05C38
Abstract

Aims: Try to prove the $n$-dimensional balanced hypercube $BH_n$ is $(2n-2)$-fault-tolerant-prescribed hamiltonian laceability. Methods: Prove it by induction on $n$. It is known that the assertation holds for $n\in\{1,2\}$. Assume it holds for $n-1$ and prove it holds for $n$, where $n\geq 3$. If there are $2n-3$ faulty links and they are all incident with a common node, then we choose some dimension such that there is one or two faulty links and no prescribed link in this dimension; Otherwise, we choose some dimension such that the total number of faulty links and prescribed links does not exceed $1$. No matter which case, partition $BH_n$ into $4$ disjoint copies of $BH_{n-1}$ along the above chosen dimension. Results: On the basis of the above partition of $BH_n$, in this manuscript, we complete the proof for the case that there is at most one faulty link in the above chosen dimension., Comment: 51pages, 0 figure

Published
2022

31. Heterogeneous System Data Storage and Retrieval Scheme Based on Blockchain

Author

Zhang, Ni, Ma, BaoQuan, Wang, Peng, Lei, XuHua, Cheng, YeJian, Li, JiaXin, Huai, XiaoYong, Shen, ZhiWei, Song, NingNing, Wang, Long, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Qiu, Meikang, editor, Lu, Zhihui, editor, and Zhang, Cheng, editor

Published
2023
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