A hypergraph exists that is colorable by each of given palettes but not by an additional palette exactly when no palette homomorphism exists to that additional palette or its inverse.
Erd˝ os:On the combinatorial problems which I would most like to see solved, Combinatorica1(1981), 25–42
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Uniform Tur\'an density -- palette classification
A hypergraph exists that is colorable by each of given palettes but not by an additional palette exactly when no palette homomorphism exists to that additional palette or its inverse.