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The k-ary n-cube is one of the most popular interconnection networks for parallel and distributed systems. Given an edge set in the k-ary n-cube, which conditions guarantee the existence of a Hamiltonian cycle in the k-ary n-cube containing the edge set? In this paper, we prove for n⩾2 and k⩾3 that every matching having at most 3n-8 edges is contained in a Hamiltonian cycle in the k-ary n-cube. Also,...
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