论文标题
平衡超振管的最佳边缘耐受性耐受性的汉密尔顿可撕裂性
Optimal edge fault-tolerant-prescribed hamiltonian laceability of balanced hypercubes
论文作者
论文摘要
目的：尝试证明$ n $维平衡的hypercube $ bh_n $是$（2n-2）$ - 容忍性的汉密尔顿可渗透性。方法：通过$ n $的归纳来证明这一点。众所周知，该断言为$ n \ in \ {1,2 \} $。假设它以$ n-1 $为单位，并证明它以$ n $为单位，其中$ n \ geq 3 $。如果有$ 2N-3 $故障的链接，并且它们都是带有通用节点的事件，那么我们选择一些维度，以便在此维度中有一个或两个故障的链接，没有规定的链接；否则，我们选择一些维度，以使故障链接的总数和规定的链接不超过$ 1 $。无论哪种情况，分区$ bh_n $ to $ 4 $划分的$ bh_ {n-1} $沿着上述尺寸的副本。结果：根据上述$ bh_n $的分区，在本手稿中，我们完成了以上选择的维度中最多有一个错误的链接的证据。
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.
