A generalization of the Hajnal-Szemerédi theorem for uniform hypergraphs (Q2353014)

It is well known that the chromatic number of a graph cannot exceed its maximum degree plus one. In the case of \(k\)-uniform hypergraphs, it is known that there exists an \(r\)-coloring if the maximum degree does not exceed an expression depending on \(k\) and \(r\). There is also a known upper bound for the maximum degree of \(k\)-uniform hypergraphs that guarantees the existence of an \(r\)-equitable coloring. In this paper, the author improves the known upper bound for the maximum degree that guarantees that a \(k\)-hypergraph has a 2-equitable coloring.