By the inductive hypothesis an in-order traversal of The remaining cases for an internal node n can be dealt with in a similar way.
finally, from this property it follows that the set of vertices introduced by the anchored nodes within T n is [i, j], since [i, j] contains all and only the symbols Definition 2 places constraints on the tree structure of the tree decomposition T, based on the ordering w, but does not refer to the contents of the bag at each node of T. the problem of finding a tree decomposition of G can be broken into the two problems of, first, finding a parse tree for w and, second, identifying the vertices of G to include in the bag at each node of T. Notation.