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A hypergraph is said to be 1‐Sperner if for every two hyperedges the smallest of their two set differences is of size one. We present several applications of ‐Sperner hypergraphs to graphs. First, we consider several ways of associating hypergraphs to graphs, namely, vertex cover, clique, independent set, dominating set, and closed neighborhood hypergraphs. For each of them, we characterize graphs...
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