Necessary Spectral Conditions for Coloring Hypergraphs

Franklin H. J. Kenter

Hoffman proved that for a simple graph $G$, the chromatic number $\chi (G)$ obeys $\chi (G)\le 1-\frac{{\lambda }_1}{{\lambda }_n}$ where ${\lambda }_1$ and ${\lambda }_n$ are the maximal and minimal eigenvalues of the…