RT Journal Article
T1 Coarse distinguishability of graphs with symmetric growth
A1 Álvarez López, Jesús Antonio
A1 Barral Lijó, Ramón
A1 Nozawa, Hiraku
K1 Graph
K1 Coloring
K1 Distinguishing
K1 Coarse
K1 Growth
K1 Symmetry
AB Let $X$ 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 $\lim d(x_n,f(x_n))=\infty$.
PB University of Primorska in collaboration with the Slovenian Society of Discrete and Applied Mathematics, Society of Mathematicians, Physicists and Astronomers of Slovenia and the Institute of Mathematics, Physics and Mechanics
YR 2021
FD 2021-08-19
LK http://hdl.handle.net/10347/32030
UL http://hdl.handle.net/10347/32030
LA eng
NO Álvarez 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/10.26493/1855-3974.2354.616
NO Canon Foundation in Europe fellowship [B.L.]; JSPS KAKENHI Grant Number 17K14195 and20K03620 [H.N.]; Program for the Promotion of International Research by Ritsumeikan University[A.L., B.L., H.N.]; FEDER/Ministerio de Ciencia, Innovación y Universidades/AEI/MTM2017-89686-P, Xunta de Galicia/ED431C 2019/10 [A.L.].
DS Minerva
RD 28 abr 2026