Abstract
In this note, we define completely independent spanning trees. We say that T 1, T 2,…, T k are completely independent spanning trees in a graph H if for any vertex r of H, they are independent spanning trees rooted at r. We present a characterization of completely independent spanning trees. Also, we show that for any k-vertex-connected line digraph L( G), there are k completely independent spanning trees in the underlying graph of L( G). At last, we apply our results to de Bruijn graphs, Kautz graphs, and wrapped butterflies.
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