Structure Trees and Networks

Abstract

In this paper it is shown that for any network there is a uniquely determined network based on a structure tree that provides a convenient way of determining a minimal cut separating a pair $s, t$ where each of $s, t$ is either a vertex or an end in the original network. A Max-Flow Min-Cut Theorem is proved for any network. In the case of a Cayley Graph for a finitely generated group the theory provides another proof of Stallings' Theorem on the structure of groups with more than one end.