Completely independent spanning trees in torus networks

Let T1, T2, ..., Tk be spanning trees in a graph G. If for any two vertices u, v in G, the paths from u to v in T1, T2, ..., Tk are pairwise internally disjoint, then T1, T2, ..., Tk are completely independent spanning trees in G. Completely independent spanning trees can be applied to fault-tolerant communication problems in interconnection networks. In this article, we show that there are two completely independent spanning trees in any torus network. Besides, we generalize the result for the Cartesian product. In particular, we show that there are two completely independent spanning trees in the Cartesian product of any 2-connected graphs. (c) 2011 Wiley Periodicals, Inc. NETWORKS, 2012