Two new homomorphism dualities and lattice operations

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