Fault-free Hamiltonian cycles passing through a linear forest in ternary n-cubes with faulty edges

A linear forest in a graph is a subgraph each component of which is a path. In this paper, we investigate the existence of a Hamiltonian cycle passing through a linear forest in a ternary n-cube Qn3 (n≥2) with faulty edges. Let F be a faulty edge set of Qn3 and L be a prescribed linear forest in Qn3−F. If |E(L)|≤2n−1 and |F|≤n−(⌊|E(L)|/2⌋+1), then there is a Hamiltonian cycle passing through L in Qn3−F.