# Article

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Keywords:
relation; compactness
Summary:
In this paper we generalize classical 3-set theorem related to stable partitions of arbitrary mappings due to Erd\H{o}s-de Bruijn, Katětov and Kasteleyn. We consider a structural generalization of this result to partitions preserving sets of inequalities and characterize all finite sets of such inequalities which can be preserved by a small'' coloring. These results are also related to graph homomorphisms and (oriented) colorings.
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