On embedding cycles into faulty twisted cubes

The twisted cube TQn is an alternative to the popular hypercube network. Recently, some interesting properties of TQn were investigated. In this paper, we study the pancycle problem on faulty twisted cubes. Let fe and fv be the numbers of faulty edges and faulty vertices in TQn, respectively. We show that, with fe + fv ⩽ n − 2, a faulty TQn still contains a cycle of length l for every 4 ⩽ l ⩽ ∣V(TQn)∣ − fv and odd integer n ⩾ 3.