Abstract
The Constraint Satisfaction Problem (CSP) is studied for constraints given as requirements in full graph homomorphisms. It is proved that for every finite (full) system of constraints there exists a finite duality, that is, a finite system of prohibited sources, or subobjects, equivalent with the constraint task.
The converse, however does not hold, in fact it is, rather, rare - it is a phenomenon of the Ramsey type. As an illustration we present a number of concrete finite dualities, and of the associated Ramsey phenomena.