Cocompact unfolding trees

2025/07/10 by Roman Gorazd, Gorazd, Roman
Computer Science · Mathematics · #05E16 #05E18 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Interconnection Networks and Systems

paper · pdf · doi:10.48550/arxiv.2507.07503

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Classification of Label-Regular Directed Trees up to Almost Isomorphism
• Topological full groups and t.d.l.c. completions of Thompson's V
• Topological full groups of one-sided shifts of finite type

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