Cocompact unfolding trees

Abstract

This paper will show when a rooted path tree of a finite directed rooted graph has only finitely many orbits under the action of its undirected automorphism group (i.e. when it is cocompact). This will allow us to specify which trees are almost isomorphic to cocompact trees. We will provide an algorithm that will determine this, thus mostly answering question (1) from arXiv:2212.07205.

Adapted from Thesis chapter, 30 pages, 6 figures