3 problems

Let $G$ be a countable, connected graph. An automorphism moves infinitely many edges if it does not fix infinitely many edges of $G$. A $2$-edge colouring is distinguishing if the…

Infinite motion conjecture for graphs. If $\operatorname{Aut}(G)$ has infinite motion, then

Infinite motion conjecture for permutation groups. If $A$ is closed and subdegree-finite with infinite motion, then