On the structure of vertex cuts separating the ends of a graph

Abstract

Dinits, Karzanov and Lomonosov showed that the minimal edge cuts of a finite graph have the structure of a cactus, a tree-like graph constructed from cycles. Evangelidou and Papasoglu extended this to minimal cuts separating the ends of an infinite graph. In this paper we show that minimal vertex cuts separating the ends of a graph can be encoded by a succulent, a mild generalization of a cactus that is still tree-like. We go on to show that the earlier cactus results follow from our work.