Embedding Hamiltonian cycles in alternating group graphs under conditional fault model

In this paper, assuming that each node is incident with two or more fault-free links, we show that an n-dimensional alternating group graph can tolerate up to 4n −13 link faults, where n ⩾4, while retaining a fault-free Hamiltonian cycle. The proof is computer-assisted. The result is optimal with respect to the number of link faults tolerated. Previously, without the assumption, at most 2n −6 link faults can be tolerated for the same problem and the same graph.