Figure 2

Setup of the dynamic programming on tree decompositions. A vertex u ∈ X(i) can have degree d(u) = 0 (white circle), d(u) = 1 (black circle), or d(u) = 2 (gray circle) in $G_i^S$. Vertices with d(u) = 1 are always incident with paths in $G_i^S$ (gray ellipse), forming a pairing (a permutation) P on them.