Plasticity of hyperspaces of plastic locally finite graphs

Determine whether the hyperspace of nonempty compact subsets, equipped with the Hausdorff metric induced by the unweighted path metric, is plastic for every plastic infinite connected locally finite graph.

Background

The paper proves that the hyperspace $KG$ is plastic for every connected, locally finite, regular graph and for certain nonregular graphs whose vertices of minimum degree form a finite set. The remaining case includes plastic infinite connected locally finite graphs with infinitely many vertices of minimum degree, for which the regular-graph argument and the finite-minimum criterion do not apply. The general implication from plasticity of $G$ to plasticity of $KG$ is therefore left unresolved.