How to prove whether a given matroid is a Gammoid? Statement : Given a matroid in some representation say $(E,I)$. How do we prove it is a gammoid?
For example to prove a matroid is transversal, we try to create a bipartite graph. If we are unable to(i.e. if we get some contradiction) then it is not transversal.
Similarly in cotransversal, we create a directed graph, and show all independent sets are linked to the fixed base using disjoint paths.
But if a matroid is a general gammoid, how can we prove it?
Answer according to me: One way I think is to show it is contraction of some transversal matroid(or restriction of cotransversal matroid). But how do we find that transversal(or cotransversal) matroid then?

According to Oxley, deciding whether a given matroid is a gammoid is still open. There is a way to check whether a given matroid is a strict gammoid, though, and you can find it in Oxley as well.
