對於一個二分圖G，若它包含了長度從4到｜V（G）｜的環路，則我們稱它有二元泛圈性質，其中｜V（G）｜是指圖G中頂點的個數。Fv及Fe分別為一個n-維超立方體上壞點及壞邊的集合。在這篇論文中，我們證明在一個壞點及壞邊的超立方體上(Qn – Fv– Fe)，可以找到它的二元泛圈性質（環路長度從4到｜V(Qn)｜– 2｜Fv｜），其中Fv + Fe <= n-2 . 因為Qn是分割大小相同的二分圖並且也是度數為n的正規圖，所以我們的容錯數及所找的最大環路在其最差狀況時都是最佳的。

　　A bipartite graph G is bipancyclic if it contains cycles of every even length from 4 to |V(G)| inclusive, where |V(G)| is the number of vertices of G. Let Fv(respectively, Fe) be the set of faulty vertices(respectively, faulty edges) in an n-dimensional hypercube Qn. In this paper,we show that Qn-Fv-Fe contains fault-free cycles of every even length from 4 to |V(Qn)|-2|Fv| when
|Fv|+|Fe| < = (n-2). Since Qn is bipartite of equal-size partite sets, and is regular of vertex-degree n, both the number of tolerable faults and the length of a longest fault-free cycle obtained are optimal in the worst case.

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