@inbook {IOPORT.05594503, author = {Kuo, Che-Nan and Hsieh, Sun-Yuan}, title = {Fault-free cycles in conditional faulty folded hypercubes.}, year = {2009}, booktitle = {Algorithms and architectures for parallel processing. 9th international conference, ICA3PP 2009, Taipei, Taiwan, June 8--11, 2009. Proceedings}, isbn = {978-3-642-03094-9}, pages = {439-448}, publisher = {Berlin: Springer}, doi = {10.1007/978-3-642-03095-6_42}, abstract = {Summary: An $n$-dimensional folded hypercube $FQ _{n }$ is an attractive variance of an $n$-dimensional hypercube $Q _{n }$, which is obtained by a standard hypercube with some extra edges established between its vertices. $FQ _{n }$ for any odd $n$ is known to be bipartite. In this paper, for any $FQ _{n }$ ($n \geq 2$) with at most $2n - 3$ faulty edges in which each vertex is incident with at least two fault-free edges, we prove that there exists a fault-free cycle of every even length from 4 to $2^{n }$, and when $n \geq 2$ is even, there also exists a fault-free cycle of every odd length from $n + 1$ to $2^{n } - 1$. The result is optimal with respect to the number of edges faults tolerated.}, identifier = {05594503}, }