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

Abstract

The k-ary n-cube Q_n^k (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_n^{\mathrm{3}} with faulty edges. The following result is obtained. Let E₀ (≠Ø) be a linear forest and F (≠Ø) be a set of faulty edges in Q_n^{\mathrm{3}} such that E₀ ∩ F = Øand |E₀| + |F|≤2n - 2. Then all edges of E₀ lie on a Hamiltonian cycle in Q_n^{\mathrm{3}}-F,and the upper bound 2n-2 is sharp.

Key words： Hamiltonian cycle; fault-tolerance; 3-ary n-cube; linear forest; interconnection network

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