Polychromatic coloring of a hypergraph
= Polychromatic coloring of a hypergraph
A <polychromatic coloring of a hypergraph> assigns $k$ colors to vertices so that every hyperedge contains all $k$ colors. It is stronger than merely requiring each hyperedge to be nonmonochromatic. Independently random colors and the <Lovász local lemma> can construct such colorings when edges are sufficiently large relative to their overlap degrees.