Fault-free cycles in folded hypercubes with more faulty elements

Abstract

Let FF v (respectively, FF e ) be the set of faulty vertices (respectively, faulty edges) in an n-dimensional folded hypercube FQ n . In this paper, we show that FQ n − FF v − FF e contains a fault-free cycle with length at least 2 n − 2 | FF v | if | FF e | + | FF v | ⩽ 2 n − 4 and | FF e | ⩽ n − 1 , where n ⩾ 3 . Our result improves the previously known result of [S.-Y. Hsieh, A note on cycle embedding in folded hypercubes with faulty elements, Information Processing Letters (2008), in press, doi:10.1016/j.ipl.2008.04.003] where | FF e | + | FF v | ⩽ n − 1 and n ⩾ 4 .