Álvarez López, Jesús AntonioBarral Lijó, RamónNozawa, Hiraku2024-01-292024-01-292021-08-19Álvarez López, J.A., Barral Lijó, R., Nozawa, H. (2021). Coarse distinguishability of graphs with symmetric growth. "Ars Math. Contemp.", vol. 21, n. 1, https://doi.org/10.26493/1855-3974.2354.616http://hdl.handle.net/10347/32030Let $X$ be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring $\phi\colon X\to\{0,1\}$ and some $R\in\N$ such that every automorphism $f$ preserving $\phi$ 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 $S_x$ satisfies the following condition: for every non-identity automorphism $f\in S_x$, there is a sequence $x_n$ such that $\lim d(x_n,f(x_n))=\infty$.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/GraphColoringDistinguishingCoarseGrowthSymmetry110206 Fundamentos de matemáticasjournal article10.26493/1855-3974.2354.616open access