An algebraic formulation of hypergraph colorings (Q6106296)

Summary: A hypergraph is properly vertex-colored if no edge contains vertices which are assigned the same color. We provide an algebraic formulation of the \(k\)-colorability of uniform and non-uniform hypergraphs. This formulation provides an algebraic algorithm, via Gröbner bases, which can determine whether a given hypergraph is \(k\)-colorable or not. We further study new families of \(k\)-colorings with additional restrictions on permissible colorings. These new families of colorings generalize several recently studied variations of \(k\)-colorings.