Coarse distinguishability of graphs with symmetric growth

Jesús Antonio Álvarez López, Ramón Barral Lijó, Hiraku Nozawa

Abstract


Let X be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring ϕ: X → {0, 1} and some R ∈ ℝ 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)) = ∞.


Keywords


Graph, coloring, distinguishing, coarse, growth, symmetry

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DOI: https://doi.org/10.26493/1855-3974.2354.616

ISSN: 1855-3974

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