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Fault-free Hamiltonian cycles passing through a prescribed linear forest in 3-ary n-cube with faulty edges

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Abstract

The k-ary n-cube Q k n (n ⩾ 2 and k ⩾ 3) is one of the most popular interconnection networks. In this paper, we consider the problem of a faultfree Hamiltonian cycle passing through a prescribed linear forest (i.e., pairwise vertex-disjoint paths) in the 3-ary n-cube Q 3 n with faulty edges. The following result is obtained. Let E 0 (≠ ∅) be a linear forest and F (≠= ∅) be a set of faulty edges in Q 3 n such that E 0 ∩ F = ∅ and |E 0| + |F| ⩽ 2n − 2. Then all edges of E 0 lie on a Hamiltonian cycle in Q 3 n − F, and the upper bound 2n − 2 is sharp.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, China

    Xie-Bin Chen

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  1. Xie-Bin Chen
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Correspondence to Xie-Bin Chen.

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Chen, XB. Fault-free Hamiltonian cycles passing through a prescribed linear forest in 3-ary n-cube with faulty edges. Front. Math. China 9, 17–30 (2014). https://doi.org/10.1007/s11464-013-0344-4

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  • DOI: https://doi.org/10.1007/s11464-013-0344-4

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