On the star forest polytope

A star forest is a collection of vertex-disjoint trees of depth at most 1, and its size is the number of leaves in all its components. A spanning star forest of a given graph G is a spanning subgraph of G that is also star forest. The spanning star forest problem (SSFP for short) [10] is to find maximum size spanning star forest of given graph. Let define some graph G = (V;E), to every star forest we associate a vector x^F . x^F (e) = 1 if e ∈ F and x^F (e) = 0 otherwise. x^F is the incident vector of spanning star forest F. The convex hull of all spanning star forest incident vectors is called a spanning star forest polytope, denoted SFP(G). In this paper we are mainly interested on complete characterization of SFP(G).