497 research outputs found
Coarse distinguishability of graphs with symmetric growth
Let be a connected, locally finite graph with symmetric growth. We prove
that there is a vertex coloring and some
such that every automorphism preserving is
-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 satisfies the following
condition: for every non-identity automorphism , there is a sequence
such that
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