Independent Spanning Trees on Two-dimension Tori

Two spanning trees of a given graph G having the same root r are said to be independent if for every vertex v of G the two paths from r to v along these two trees are vertex-disjoint. A set of spanning trees of G is said to be independent if they are pairwise independent. A two-dimension torus is a mesh with wrap-around connections in both the vertical and horizontal directions. Any two-dimension torus has four independent spanning trees rooted at the same vertex. In this paper, a linear time algorithm is proposed to construct four independent spanning trees on a two-dimension torus.