Vertex cover: The nodes of the tree T cover all the vertices of G: Edge cover: Each edge in G is included in some node of T. That is, for all edges (u, v) ∈ E, there exists an n ∈ N with u, v ∈ Bag(n).
running intersection: The nodes of T containing a given vertex of G form a connected subtree of T. for all n, n 1 , The width of a tree decomposition T is max n∈N |bag(n)| − 1.