Before revision:  We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw +  1 when tw is the treewidth\le  .
After revision:  We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw + 1 ) For any G, there is an optimal top separator S such that |S|\le .