  A graph G is said to be 2-distinguishable if there is a 2-labeling of its
vertices which is not preserved by any nontrivial automorphism of G. We show
that every locally finite graph with infinite motion and growth at most
O(2^((1-\varepsilon) \sqrt(n)/2)) is 2-distinguishable. Infinite motion means
that every automorphism moves infinitely many vertices and growth refers to the
cardinality of balls of radius n.
