The method you currently use now is called adjacency list model.
Another model to store hierarchical data in a (relational) database is the nested set model. Its implementation in SQL databases is well known. Also see this article for the modified preorder tree traversal algorithm.
A very simple method: you could store a path per object – with those it should be easy to query trees in NOSQL databases:
{ path: "Color", ... }
{ path: "Color.Red", ... }
{ path: "Color.Red.Apple", ... }
{ path: "Color.Red.Cherry", ... }
When nodes will be removed or renamed some paths must be updated. But in general, this method looks promising. You just have to reserve a special character as separator. The storage space overhead should be negligible.
edit: this method is called materialized path
Finally, here is a comparison of different methods for hierarchical data in NOSQL databases.