In general, the class of threshold hypergraphs and decomposable hypergraphs are not equal. In this paper, we show however that, except for two counter examples, a decomposition hypergraph consisting of five or fewer classes is in fact threshold. In the process of showing this result, the paper generates all decomposable quotients with five or fewer classes.
Citation
Margaret A.Francel, David J.John. \(3\)-Regular Hypergraphs that are Decomposable and Threshold[J], Ars Combinatoria, Volume 067. 3-26. .