  We study the enumeration complexity of Unions of Conjunctive Queries(UCQs).
We aim to identify the UCQs that are tractable in the sense that the answer
tuples can be enumerated with a linear preprocessing phase and a constant delay
between every successive tuples. It has been established that, in the absence
of self-joins and under conventional complexity assumptions, the CQs that admit
such an evaluation are precisely the free-connex ones. A union of tractable CQs
is always tractable. We generalize the notion of free-connexity from CQs to
UCQs, thus showing that some unions containing intractable CQs are, in fact,
tractable. Interestingly, some unions consisting of only intractable CQs are
tractable too. We show how to use the techniques presented in this article also
in settings where the database contains cardinality dependencies (including
functional dependencies and key constraints) or when the UCQs contain
disequalities. The question of finding a full characterization of the
tractability of UCQs remains open. Nevertheless, we prove that for several
classes of queries, free-connexity fully captures the tractable UCQs.
