Conjunctive query containment over trees

The complexity of containment and satisfiability of conjunctive queries over finite, unranked, labeled trees is studied with respect to the axes Child, NextSibling, their transitive and reflexive closures, and Following. For the containment problem a trichotomy is presented, classifying the problems as in PTIME, coNP-complete, or -complete. For the satisfiability problem most problems are classified as either in PTIME or NP-complete.