Minimal Dominating Set Enumeration

Let G be a graph on n vertices and m edges. An edge is written xy (equivalently yx). A dominating set in G is a set of vertices D such that every vertex of G is either in D or is adjacent to some vertex of D. It is said to be minimal if it does not contain any other dominating set as a proper subset. For every vertex x let N [x] be {x} ∪ {y | xy ∈ E}, and for every S ⊆ V let N [S] := ⋃ x∈S N [x]. For S ⊆ V and x ∈ S we call any y ∈ N [x] \ N [S \ x] a private neighbor of x with respect to S. The set of minimal dominating sets of G is denoted by D(G). We are interested in an output-polynomial algorithm for enumerating D(G), i.e., listing, without repetitions, all the elements of D(G) in time bounded by p(n+m, ∑