A hypergraph H is called a hypertree, 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. 
Since a tree is a hypertree, hypertrees may be seen as a generalization of the notion of a tree for hypergraphs. Any hypertree is isomorphic to some family of subtrees of a tree. 
A hypertree has the Helly property (2-Helly property), i.e., if any two hyperedges from a subset of its hyperedges have a common vertex, then all hyperedges of the subset have a common vertex. 
The line graph of a hypertree is a chordal graph.
A hypergraph is a hypertree if and only if its dual hypergraph is conformal and chordal.