It can be verified that this is equivalent to the following statement: For every triplet of nodes i, j, k, if i ⇒ j and i ⇒ k, then either j ⇒ k or k ⇒ j (or both).
this constraint can be stated in a linear form: adding this new type of constraint to the ILP given in Equation 3results in a formulation for Max-trans-Forest: A natural question is whether there is a simpler (polynomial) solution for Max-trans-Forest that avoids the need for an ILP solver.