On spanning tree congestion of graphs

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