Each node n ∈ N is associated with a set Bag(n) ⊆ V, referred to as a bag, in such a way that the following properties are all satisfied.
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. for all edges (u, v) ∈ E, there exists an n ∈ N with u, v ∈ Bag(n).