Quite sure your version of PGX come with PGQL 1.1, so you can check PGQL 1.1 Specification - 21 December 2017 | PGQL · Property Graph Query Language .
The function "java_regexp_like" gives you something even more powerful than LIKE, but ... being a regexp it will be more 'challenging' to write.
Yes, java_regexp_like is a very good solution!
In case you are also searching for something like text search, I would like to take this opportunity to point to a new beta feature we have in the recently released PGX 19.1.0: external stores ( https://docs.oracle.com/cd/E56133_01/latest/reference/api/external-stores.html ). One can use this to connect PGX and Elasticsearch and then call a specialized PGQL text_search() function for some rudimentary text search support. Please note this is a beta feature and subject to changes in the future (for example the text_search function may change form).