Fig. 6

(a) Color assignation rules for vertices, when going down-tree. (b) Sketch of the general pattern our color assignation rules create on \(\mathcal {T}_u\), the subtree of bags containing a given vertex u. Looking at it top-down: any orange part may only be a path starting at the root of the sub-tree. Some red sub-trees may branch off from it. On the sketch, at the end of the orange path, the vertex turns green. This top-most green vertex is at the root of a green sub-tree, with potential red sub-trees branching off from it