We define and investigate the notion of a decomposable hypergraph, showing that such a hypergraph always is conformal, that is, can be viewed as the class of maximal cliques of a graph. We further show that the clique hypergraph of a graph is decomposable if and only if the graph is triangulated and characterise such graphs in terms of a combinatorial identity.
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Lauritzen et al. (1984) studied this question.
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