Regular families of forests, antichains and duality pairs of relational structures

Erdős, Péter and Pálvölgyi, Dömötör and Tardif, C. and Tardos, Gábor (2016) Regular families of forests, antichains and duality pairs of relational structures. COMBINATORICA. ISSN 0209-9683 (In Press)

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Abstract

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 [6] that gave several examples of infinite-finite antichain duality pairs of directed graphs and [7] giving a complete characterization for caterpillar dualities. © 2016 János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg

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