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Hypergraphs are generalizations of graphs, where edges can be made of more than two vertices.

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When does a hypergraph represent maximal independent sets?

Then, we can view the set of maximal independent sets (or the set of maximal cliques) as a hypergraph $H = (V, E')$. … When is the converse true, namely, when does a hypergraph correspond to a set of maximal independent sets? …