In this paper, we study the fault-tolerant capability of hypercubes with respect to the hamiltonian property based on the concept of forbidden faulty sets. We show, with the assumption that each vertex is incident with at least three fault-free edges, that an [Formula: see text]-dimensional hypercube contains a fault-free hamiltonian cycle, even if there are up to [Formula: see text] edge faults. Moreover, we give an example to show that the result is optimal with respect to the number of edge faults tolerated.

中文翻译：

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禁止故障集模型下故障超立方体的哈密顿循环嵌入

在本文中，我们基于禁止错误集的概念研究了超立方体关于哈密顿性质的容错能力。我们表明，假设每个顶点都与至少三个无故障边相关，[公式：见文本]维超立方体包含一个无故障哈密顿循环，即使有多达 [公式：见文本] 边缘缺陷。此外，我们给出了一个例子来表明结果对于允许的边缘错误的数量是最优的。