Brualdi and Hollingsworth conjectured that, for even n, in a proper edge coloring of Kn using precisely n − 1 colors, the edge set can be partitioned into n2 spanning trees which are rainbow (and hence, precisely one edge from each color class is in each spanning tree). They proved that there always are two edge disjoint rainbow spanning trees. Kaneko, Kano and Suzuki improved this to three edg...

In this paper, we propose an algorithm for nding all the spanning trees in undirected graphs. The algorithm requires O(n +m + n) time and O(n +m) space, where the given graph has n vertices, m edges and spanning trees. For outputting all the spanning trees explicitly, this algorithm is optimal.