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 + td(G \backslash S), where td(G) denotes the treedepth of G. Then, we have two theoretical results on the size of optimal top separators. ( 1 when tw is the treewidth\le .