A cactus theorem for end cuts

Abstract

Dinits-Karzanov-Lomonosov showed that it is possible to encode all minimal edge cuts of a graph by a tree-like structure called a cactus. We show here that minimal edge cuts separating ends of the graph rather than vertices can be "encoded" also by a cactus. As a corollary, we obtain a new proof of Stallings' ends theorem. We apply our methods to finite graphs as well and we show that several types of cuts can be encoded by cacti. © 2014 World Scientific Publishing Company