Displaying the structure of the space of ends of infinite graphs by trees
Johannes Carmesin · arXiv (Cornell University) · 2014
Settling a problem of Diestel from 1992, we prove that every graph G has a tree-decomposition (T, Pt|t ∈ V (T)) of finite adhesion such that the ends of T are the undominated ends of G. First, we use this to prove that the topological cycles of an arbitrary infinite graph induce a matroid, which in general is neither finitary nor cofinitary. Second, we use this to construct for every graph an end-faithful spanning tree for the set of undominated ends. 1