Hoffman's bound for hypergraphs

One of the best-known results in spectral graph theory is the inequality of Hoffman $$\chi\left( G\right) \geq1-\frac{\lambda\left( G\right) }{\lambda_{\min }\left( G\right) },$$ where $\chi\left( G\right)$ is the chromatic number of a graph $G$ and $\lambda\left( G\right) ,$ $\lambda_{\min}\left( G\right)$ are the largest and the smallest eigenvalues of its adjacency matrix. In this note Hoffman's inequality is extended to weighted uniform $r$-graphs for every even $r$.