An Algorithm for Enumerating All Spanning Trees of a Directed Graph
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We present an O(NV + V 3 ) time algorithm for enumerating all spanning trees of a directed graph. This improves the previous best known bound of O(NE + V+E)  when V 2 =o(N) , which will be true for most graphs. Here, N refers to the number of spanning trees of a graph having V vertices and E edges. The algorithm is based on the technique of obtaining one spanning tree from another by a series of edge swaps. This result complements the result in the companion paper  which enumerates all spanning trees in an undirected graph in O(N+V+E) time.
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