Minimum spanning trees on random networks

We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Because of this geometric universality, we are able to charac terize the energy of MST using a scaling distribution [P(epsilon)] found us ing uniform disorder. We show that the MST energy for other disorder distri butions is simply related to P(epsilon). We discuss the relationship to inv asion percolation, to the directed polymer in a random media, to uniform sp anning trees, and also the implications for the broader issue of universali ty in disordered systems.