\(3\)-Regular Hypergraphs that are Decomposable and Threshold

Abstract

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.