We exhibit a 5-uniform hypergraph that has no polychromatic 3-coloring, but all its restricted subhypergraphs with edges of size at least 3 are 2-colorable. This disproves a bold conjecture of Keszegh and the author, and can be considered as the first step to understand polychromatic colorings of hereditary hypergraph families better since the seminal work of Berge. We also show that our method cannot give hypergraphs of arbitrary high uniformity, and mention some connections to panchromatic colorings.

翻译：我们构造了一个5-一致超图，它不存在多色3-染色，但其所有边大小至少为3的限制子超图都是2-可染色的。这一结果否证了Keszegh与本文作者提出的一个大胆猜想，并可视为自Berge开创性工作以来，深化对遗传超图族多色染色理解的第一步。我们还证明了该方法无法构造出任意高一致性的超图，并提及了与全色染色的若干联系。