In this paper, we present some properties on chromatic polynomials ofhypergraphs which do not hold for chromatic polynomials of graphs. We firstshow that chromatic polynomials of hypergraphs have all integers as their zerosand contain dense real zeros in the set of real numbers. We then prove that forany multigraph $G=(V,E)$, the number of totally cyclic orientations of $G$ isequal to the value of $|P(H,-1)|$, where $P(H,\lambda)$ is the chromaticpolynomial of a hypergraph $H$ which is constructed from $G$. Finally we showthat the multiplicity of root "$0$" of $P(H,\lambda)$ may be at least $2$ forsome connected hypergraphs $H$, and the multiplicity of root "$1$" of$P(H,\lambda)$ may be $1$ for some connected and separable hypergraphs $H$ andmay be $2$ for some connected and non-separable hypergraphs $H$.
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机译：在本文中，我们介绍了超级图的色多项式的一些性质，这些性质不适用于图的色多项式。我们首先显示超图的色多项式具有所有整数作为其零，并且在实数集中包含密集的实零。然后，我们证明对于任何多图$ G =（V，E）$，$ G $的完全循环取向的数量等于$ | P（H，-1）| $的值，其中$ P（H，\ lambda $是从$ G $构造的超图$ H $的色多项式。最后，我们表明，对于某些连通的超图$ H $，根“ $ 0 $”的多重性可能至少为$ 2 $，而根“ $ 1 $”的多重性$ P（H，\对于某些连通和可分离的超图$ H $，λ可能是$ 1 $；对于某些连通和不可分离的超图$ H $，λ可能是$ 2 $。
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