On the existence of edge-disjoint 2-connected spanning subgraphs

We prove that every 6 k -connected graph contains k edge-disjoint rigid (and hence 2-connected) spanning subgraphs. By using this result we can settle special cases of two conjectures, due to Kriesell and Thomassen, respectively: we show that every 12 -connected graph G has a spanning tree T for which G - E ( T ) is 2 -connected, and that every 18 -connected graph has a 2 -connected orientation.