On spanning tree congestion of graphs

Let GG be a connected graph and TT be a spanning tree of GG. For e∈E(T)e∈E(T), the congestion   of ee is the number of edges in GG connecting two components of T−eT−e. The edge congestion of  GGin  TT is the maximum congestion over all edges in TT. The spanning tree congestion of  GG is the minimum congestion of GG in its spanning trees. In this paper, we show the spanning tree congestion for the complete kk-partite graphs and the two-dimensional tori. We also address lower bounds of spanning tree congestion for the multi-dimensional grids and the hypercubes.