Two new homomorphism dualities and lattice operations

The study of constraint satisfaction problems definable in various fragments of Datalog has recently gained considerable importance. We consider constraint satisfaction problems that are definable in the smallest natural recursive fragment of Datalog - monadic linear Datalog with at most one EDB per rule, and also in the smallest non-linear extension of this fragment. We give combinatorial and algebraic characterisations of such problems, in terms of homomorphism dualities and lattice operations, respectively. We then apply our results to study graph H-colouring problems.