Every infinitely edge-connected graph contains the Farey graph or T_ℵ0 ∗ t as a minor

2020/04/14 by Jan Kurkofka, Kurkofka, Jan
Computer Science · Mathematics · #05C10 (Secondary) #05C40 #05C55 #05C63 (Primary) #05C83 #Advanced Graph Theory Research #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Graph theory and applications #Group Theory (math.GR) #Interconnection Networks and Systems #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2004.06710

openalex publication_date 2020/04/14 · openalex created_date 2020/04/24 · openalex updated_date 2026/07/28

Abstract

We show that every infinitely edge-connected graph contains the Farey graph or T_ℵ0 ∗ t as a minor. These two graphs are unique with this property up to minor-equivalence.

Related

• The Farey graph is uniquely determined by its connectivity
• Ubiquity and the Farey graph
• Quickly excluding a non-planar graph
• Small Complete Minors Above the Extremal Edge Density
• Universal planar graphs for the topological minor relation