Formally, we have cont T (b) = {src D (edg T (b)), tar D (edg T (b))}.
furthermore, we require that the mapping edg T is a bijection between the leaves of T and the edges of D. every edge of D is introduced by a unique leaf b of T. Note that, because edg T is a bijection, for every edge e ∈ E D we have that edg −1 T (e) yields the unique leaf b of T such that edg T (b) = e. In Appendix A, Theorem 8, we show that if a graph has a tree decomposition of width k, then there exists a binary tree decomposition of the same graph also having width k. Our method of binarization is illustrated in figure 16 and explained in the following.