A hypergraph H is a hypertree if and only if it has the Helly property and its line graph is a chordal graph. A hypergraph H is a hypertree if and only if its dual hypergraph H* is conformal and the 2-section graph of H* is chordal.[7] A hypergraph is a hypertree if and only if its dual hypergraph is alpha-acyclic in the sense of Fagin.[8]