Leaf-reparenting sufficiency for transforming spanning trees in polycube reconfiguration

Determine whether transforming one spanning tree into another can be achieved solely by leaf reparenting operations within the cube-sliding refolding framework for tree-shaped polycubes.

Background

For tree-shaped polycubes, the paper realizes slide and rotate operations for leaf cubes and provides an O(n^2)-step reconfiguration to a line. Extending these operations to nonleaf cubes is challenging.

The authors suggest transforming one spanning tree to another as a possible approach but explicitly note it is unclear whether leaf reparenting alone suffices to achieve such transformations.