The independence number, coloring number and related parameters are investigated in the setting of oriented hypergraphs using the spectrum of the normalized Laplace operator. For the independence number, both an inertia–like bound and a ratio–like bound are shown. A Sandwich Theorem involving the clique number, the vector chromatic number and the coloring number is proved, as well as a lower bound for the vector chromatic number in terms of the smallest and the largest eigenvalue of the normalized Laplacian. In addition, spectral partition numbers are studied in relation to the coloring number.

中文翻译：

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为定向超图的归一化拉普拉斯算子着色

使用归一化拉普拉斯算子的谱研究了定向超图设置中的独立数、着色数和相关参数。对于独立数，显示了类惯性边界和类比率边界。证明了包含团数、向量色数和着色数的三明治定理，并根据归一化拉普拉斯算子的最小和最大特征值给出了向量色数的下界。此外，还研究了与着色数相关的光谱分区数。