Hamiltonian Cycle Embeddings in Faulty Hypercubes Under the Forbidden Faulty Set Model

Abstract

In this paper, we study the fault-tolerant capability of hypercubes with respect to the hamiltonian property based on the concept of forbidden faulty sets. We show, with the assumption that each vertex is incident with at least three fault-free edges, that an [Formula: see text]-dimensional hypercube contains a fault-free hamiltonian cycle, even if there are up to [Formula: see text] edge faults. Moreover, we give an example to show that the result is optimal with respect to the number of edge faults tolerated.