Conditions For Degree Sequences to Be Realisable By 3-Uniform Hypergraphs

A degree sequence which is realisable by a \(3\)-uniform hypergraph is called \(3\)-graphic. Seven necessary conditions, one sufficient condition, and one equivalent condition for degree sequences to be \(3\)-graphic are derived. Moreover, four special classes of degree sequences are examined. For each class an equivalent condition for the sequences in this class to be \(3\)-graphic is derived. Using these conditions, all the \(3\)-graphic degree sequences of length at most seven have been determined.