Geodesic
Coarse distinguishability of graphs with symmetric growth
Ars Mathematica Contemporanea, Tome 21 (2021) no. 1, article no. 06, 18 p.

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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)) = ∞.
DOI : 10.26493/1855-3974.2354.616
Keywords: Graph, coloring, distinguishing, coarse, growth, symmetry 
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Jesús Antonio Álvarez López; Ramón Barral Lijó; Hiraku Nozawa. Coarse distinguishability of graphs with symmetric growth. Ars Mathematica Contemporanea, Tome 21 (2021) no. 1, article  no. 06, 18 p. doi : 10.26493/1855-3974.2354.616. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2354.616/

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