Abstract:In this paper we generalize classical 3-set theorem related to stable partitions of arbitrary mappings due to Erd\H {o}s-de Bruijn, Kat\v etov 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.
Keywords: relation, compactness
AMS Subject Classification: 05C05, 05C99