Embedding Hamiltonian cycles in alternating group graphs under conditional fault model

Abstract

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 4 n − 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 2 n − 6 link faults can be tolerated for the same problem and the same graph.