Conditional fault Hamiltonicity of the complete graph

Let Kn denote a complete graph of n nodes. In this paper, assuming that each vertex is incident with at least two fault-free links, we show that Kn can tolerate up to 2n−8 edge faults, while retaining a fault-free Hamiltonian cycle, where n⩾4 and n∉{7,9}. When contains a fault-free Hamiltonian cycle if there are up to 2n−9 edge faults. The result is optimal with respect to the number of edge faults tolerated.