Enforce Referential Integrity on Materialized Path?

Yes, you have to enforce data integrity yourself in the DAL when you use either Materialized Path or Nested Sets solutions for hierarchical data.

Adjacency List supports referential integrity, and this is true also for a design I call "Closure Table" (Tropashko calls this design "transitive closure relation").

"Materialized path" as presented by Vadim Tropashko in that article, introduces the notion of order into a relation ("Jones is the second member".).

"Materialized path" is nothing but "some form of materialized view" on the transitive closure, and therefore suffers all and exactly the same problems as any other "materialized view", except that matters are algorithmically worse precisely because of the involvement of a closure.

SQL is almost completely powerless when constraints-on-a-closure are in play. (Meaning : yes, SQL requires you to do everything yourself.) It's one of those areas where the RM shows the maximum of its almost unlimited power, but SQL fails abysmally, and where it is such a shame that the majority of people mistake SQL for being relational.

(@Bill Karwin : I'd like to be able to give you +1 for your remark on the relation between the depth of the trees and the result on performance. There are no known algorithms to compute closures that perform well in the case of trees with "crazy" depths. It's an algorithmic problem, not an SQL nor a relational one.)

EDIT

Yes, RM = Relational Model

In the materialized path model you can use arbitrary strings (maybe unicode strings to allow more than 256 children) instead of special strings of form "x.y.z". The id of the parent is then the id of the direct children with the last character removed. You can easily enforce this with a check constraint like (my example works in PostgreSQL)

check(parent_id = substring(id from 1 for char_length(id)-1)),

within your create table command. If you insist on strings of form "x.y.z", you'll have to play around with regular expressions, but I'd guess it's possible to find a corresponding check constraint.