# Analog of Reed's conjecture for hypergraph

Reed's $$\omega$$,$$\Delta$$, $$\chi$$ conjecture proposes that every graph has $$\chi \leq \lceil \tfrac 12(\Delta+1+\omega)\rceil$$. Here $$\chi$$ is the chromatic number, $$\Delta$$ is the maximum degree, and $$\omega$$ is the clique number.

Is there any similar theorem or conjecture that has to do with hypergraph colorings? That is where the vertices can be colored in $$\chi$$ colors such that no edge is monochromatic.

More helpful for me is the case of coloring where every k-edge has k different colors (Rainbow coloring).