Hypertree

In other words, H is a hypertree if there exists a tree T such that every hyperedge of H is the set of vertices of a connected subtree of T.[1] Hypertrees have also been called arboreal hypergraphs[2] or tree hypergraphs.

Therefore, hypertrees may be seen as a generalization of the notion of a tree for hypergraphs.

[5] By results of Duchet, Flament and Slater[6] hypertrees may be equivalently characterized in the following ways.

It is possible to recognize hypertrees (as duals of alpha-acyclic hypergraphs) in linear time.

[9] The exact cover problem (finding a set of non-overlapping hyperedges that covers all the vertices) is solvable in polynomial time for hypertrees but remains NP-complete for alpha-acyclic hypergraphs.