Hamiltonian cycles and paths in faulty twisted hypercubes

Abstract

The n-dimensional twisted hypercube Hn is obtained from two copies of the (n−1)-dimensional twisted hypercube Hn−1 by adding a special perfect matching between the vertices of these two copies of Hn−1. The twisted hypercube is a new variant of hypercubes with asymptotically optimal diameter introduced by X.D. Zhu. In this paper, we show that Hn has a fault-free Hamiltonian cycle if the number of faulty edges and/or vertices is no more than n−2, and it has a fault-free Hamiltonian path between any pair of non-faulty vertices if the number of faulty edges and/or vertices is no more than n−3.