Multiple independent spanning trees have applications to fault-tolerant and data broadcasting in distributed networks. There is a conjecture on independent spanning trees: any n-connected graph has n independent spanning trees rooted at an arbitrary vertex. The conjecture has been confirmed only for n-connected graphs with n ≤ 4, and still open for arbitrary n-connected graphs when n ≥ 5. In this paper, we confirm the conjecture for the n-dimensional twisted-cube TNn by providing an O(NlogN) algorithm to construct n independent spanning trees rooted at any vertex, where N denotes the number of vertices in TNn.
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机译：多个独立的生成树具有在分布式网络中容错和数据广播的应用程序。 在独立的生成树上有一个猜想：任何n连接的图表都有n个独立的跨越树，植根于任意顶点。 猜想仅针对N＆＃x2264的n连接的图表确认; 4，仍然在n＆＃x2265时打开任意n连接的图表; 5.在本文中，我们通过提供O（nlogn）算法来确认N维转捻 - 立方体TN N 的猜想，以构建植根于任何顶点的独立生成树，其中n表示 TN N 中的顶点数。
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