大故障模型下扭曲类超立方体网络的Hamilton连通性
Hamiltonian Connectivity of Twisted Hypercube-Like Networks under the Large Fault Model
摘要：
扭曲超立方体网络（Twistedhypercube-like networks，THLN）是一类重要的并行计算互连网络，它包含了超立方体的最流行的变体，如交叉立方体、莫比乌斯立方体、扭曲立方体和局部扭曲立方体。研究了大故障模型下THLN的容错Hamilton连通性。令$G$是$n$维THLN和$F \subseteq V(G)\bigcup E(G)$，其中$n \geq 7$和$|F| \leq 2n - 10$ .证明了对于任意两个节点$u,v \in V(G - F)$满足$u$和$v$邻居的一个简单必要条件，在$G-F$中的$u$和$v$之间存在一条Hamilton或近Hamilton路径.该结果进一步扩展了THLN的容错图嵌入能力。
英文摘要：
Twisted hypercube-like networks (THLNs) are an important class of interconnection networks for parallel computing systems, which include most popular variants of the hypercubes, such as crossed cubes, Möbius cubes, twisted cubes and locally twisted cubes. This paper deals with the fault-tolerant hamiltonian connectivity of THLNs under the large fault model. Let $G$ be an $n$-dimensional THLN and $F \subseteq V(G)\bigcup E(G)$, where $n \geq 7$ and $|F| \leq 2n - 10$. We prove that for any two nodes $u,v \in V(G - F)$ satisfying a simple necessary condition on neighbors of $u$ and $v$, there exists a hamiltonian or near-hamiltonian path between $u$ and $v$ in $G-F$. The result extends further the fault-tolerant graph embedding capability of THLNs.
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