... τ−1((T)) and Tis one of the two components of T − e. (This is well defined since, for Tbeing the other component of T − e,thesets(T),(T) form a partition of (T ).) The width of the ... branch-decomposition (T,τ) is the maximum of the widths of the edges of T ,andthebranch-width of M is the minimal width over all branch-decompositions of M.IfT hasno edge, then we take its width as ... or 6 leaves in (T ) and not all of themare single, then one of T1,T2is nice. Finally, if T0has 3 or 4 leaves in (T ) and at least 2 of them are not single, then one of T1,T2is nice...