A cactus theorem for end cuts
  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. We apply our methods to finite graphs as well and we show that several types of cuts can be encoded by cacti. 
Anastasia Evangelidou and Panos Papasoglu
math.CO