Traditionally, the way to represent a subset
of edges has been an array of booleans.
As there appear to be multiple subsets of edges,
an array of arrays of edges might be needed.
A path represented as a sequence of nodes is hard to exploain to a solver.
--
Michael
My first thought on such a task is to fix all variablee,
structural and otherwise, with nonzero reduced costs.
Unless using exact arithmetic,
that is an interesting task in itself.
Even so, I'd expect it to be better than using
a single linear constraint to implicitly fix them.
A better tactic