A “planted graph” is a simple directed graph with a specified set of vertices as sinks. Cotransversal matroids are a family of matroids that arise from planted graphs. I prove that two planted graphs give the same cotransversal matroid if and only if they can be obtained from each other by a series of local moves. Cotransversal matroids are the duals of transversal matroids, a fact that will be discussed and exploited throughout this talk.

This is joint work with Federico Ardila.