Before revision:  these are based on  the Lempel-Ziv factorization, the run-length BWT, context-free grammars and, more recently, string attractors. Labeled trees add a whole new dimension to the problem: one needs not only to compress the labels, but also the tree 's topology. On this side, less is known. Jacobson showed how to represent the topology of a tree with n nodes in 2n+o(n) bits of space (succinct) while also supporting constant-time navigation queries.
After revision:  these are based on the pre-order identifiers of all nodes reached by a path labeled with a given query pattern. Our result builds on top of the XBWT tree transform of