A hypergraph H is called a hypertree in (arboreal hypergraph in, tree hypergraph in ) if it admits a host graph T such that T is a tree, in other words if there exists a tree T such that every hyperedge of H induces a subtree in T.
By results of Duchet, Flament and Slater (see e.g.), a hypergraph is a hypertree if and only if it has the Helly property and its line graph is chordal if and only if its dual hypergraph is conformal and chordal.
Thus, a hypergraph is a hypertree if and only if its dual hypergraph is alpha-acyclic (in the sense of Fagin et al.)
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