Metric entropy of subgraph

We prove that there is some constant C so that in any finite metric graph with unit entropy, there exists a proper subgraph with entropy at least C, where C depends only on the rank of the original graph. In addition to being independently interesting from a dynamical point of view, this has applications to the study of pressure-type metrics on the Culler-Vogtmann outer space. We will not assume any advanced knowledge in either dynamics or the geometric group theory of Out(F_n). This represents joint work with Tawfiq Ahmed and Matt Clay.