Homomorphism duality pairs play a crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both sides are infinite seems to be very complex. It is also known that no finite-infinite duality pair is possible if we make the additional restriction that both classes are antichains. In this paper we characterize the infinite-finite antichain dualities and infinite-finite dualities with trees or forests on the left hand side. This work builds on our earlier papers  that gave several examples of infinite-finite antichain duality pairs of directed graphs and  giving a complete characterization for caterpillar dualities.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Mathematics