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The authors are partially supported by the Program for the Promotion of International Research by Ritsumeikan University and grants FEDER/Ministerio de Ciencia, Innovacion y Universidades/AEI/MTM2017-89686-P; and Xunta de Galicia/ED431C 2019/10. We would also like to thank the anonymous referee for a careful reading of the paper.

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Coarse distinguishability of graphs with symmetric growth

Publicat a:Ars Mathematica Contemporanea. 21 (1): P1.06- - 2021-01-01 21(1), DOI: 10.26493/1855-3974.2354.616

Autors: Alvarez Lopez, Jesus Antonio; Lijo, Ramon Barral; Nozawa, Hiraku

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Let X be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring phi: X -> {0, 1} and some R is an element of 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 nonidentity automorphism f is an element of S-x, there is a sequence x(n) such that lim d(x(n), f(x(n))) = infinity.

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