Threshold hypergraphs
Threshold graphs were introduced by \textit{V. Chvátal} and \textit{P. L. Hammer} [Ann. Discrete Math. 1, 145-162 (1977; Zbl 0384.90091)]. They gave three equivalent characterizations of these graphs. These characterizations were generalized for hypergraphs by \textit{M. Ch. Golumbic} [Combinatorics, Keszthely 1976, Colloq. Math. János Bolyai 18, 419-428 (1978; Zbl 0398.05058)]. He asked whether these were equivalent or not. The answer is negative. The authors prove this by some constructions, and give three equivalent characterizations of the most general definition from the above three generalizations. On the end of this clear style paper we can find a result on the complexity of this property.
scientific article; zbMATH DE number 3898935
scientific article