The n-dimensional folded hypercube $F{Q}_n$ interconnection network has been shown that it is bipartite for every odd $n\ge 3$, and which is non-bipartite for every even $n\ge 2$. Let $F_4=\{f_1,f_2,f_3,f_4\}$ denote the faulty set of extreme vertices from any four cycle in $F{Q}_n$. Then, we show that the fault-free cycles can be embedded in $F{Q}_n-F_4$ as follows:

1.

For $n\ge 3$, $F{Q}_n-F_4$ contains a fault-free cycle of every even length from 4 to $2^n-4$;

2.

For every even $n\ge 4$, $F{Q}_n-F_4$ contains a fault-free cycle of every odd length from $n+1$ to $2^n-5$.

The results are optimal with respect to the length type of embedded cycles in $F{Q}_n-F_4$.

中文翻译：

---

嵌入F ₄折叠超立方体的无故障循环

所述Ñ维超立方体折叠$F{问}_{ñ}$ 互连网络已经证明，每个奇数都是二分的 $ñ\ge 3$，并且每个偶数都不相等 $ñ\ge 2$。让$F_4=\{F_{\mathrm{1个}}，F_2，F_3，F_4\}$ 表示来自任何四个周期的极端顶点的错误集合 $F{问}_{ñ}$。然后，我们证明无故障周期可以嵌入到$F{问}_{ñ}-F_4$ 如下：

1。

对于 $ñ\ge 3$， $F{问}_{ñ}-F_4$ 包含从4到2的每个偶数长度的无故障循环 $2^{ñ}-4$;

2。

对于每个 $ñ\ge 4$， $F{问}_{ñ}-F_4$ 包含从 $ñ+\mathrm{1个}$ 至 $2^{ñ}-5$。

对于嵌入式循环的长度类型，结果是最佳的 $F{问}_{ñ}-F_4$。