Linkage of graphs with flows

Abstract

We prove several linkage properties of graphs with flows, generalizing some results on linkage of graphs. This translates in properties of connectedness through codimension one of certain posets. For example, the poset of flows and the posets of odd and even tropical spin curves. These posets are, respectively, the posets underlying the moduli space of roots of divisors on tropical curves and the moduli spaces of odd and even tropical spin curves.