2020/05/19 by Jesús Antonio Álvarez López, Jesús A. Álvarez López, López, Jesús Antonio Álvarez +4
Computer Science · Mathematics · #05C15 (Primary) #51F99 (Secondary) #Advanced Graph Theory Research #Automorphism #Automorphism group #Cayley graph #Combinatorics #Combinatorics (math.CO) #Conjecture #Discrete mathematics #FOS: Mathematics #Graph #Graph automorphism #Graph theory and applications #Limits and Structures in Graph Theory #Line graph #Mathematics #Metric Geometry (math.MG) #Vertex (graph theory) #Voltage graph #math.CO #math.MG #msc:05C15 #msc:51F99
paper · pdf · doi:10.48550/arxiv.2005.09716
arxiv created 2020/05/19 · openalex publication_date 2020/05/19 · arxiv updated 2020/05/21 · openalex created_date 2020/05/29 · openalex updated_date 2026/08/06
Let X be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring ϕ\colon X→\0,1\ and some R∈ℕ such that every automorphism f preserving ϕ is R-close to the identity map; this can be seen as a coarse geometric version of symmetry breaking. We also prove that the infinite motion conjecture is true for graphs where at least one vertex stabilizer Sx satisfies the following condition: for every non-identity automorphism f∈ Sx, there is a sequence xn such that lim d(xn,f(xn))=∞.