Hamiltonian path embeddings in conditional faulty k-ary n-cubes

The class of k-ary n-cubes represents the most commonly used interconnection topology for distributed-memory parallel systems. A k-ary n-cube is bipartite if and only if k is even. In this paper, we consider the faulty k-ary n  -cube with even k⩾4k⩾4 and n⩾2n⩾2 such that each vertex of the k-ary n-cube is incident with at least two healthy edges. Based on this requirement, we prove that the k-ary n  -cube contains a hamiltonian path joining every pair of vertices which are in different parts, even if it has up to 4n-54n-5 edge faults and this result is optimal.