## HyperTree:-

A hypertree H is a state tree in (arboreal hypergraph received tree hypergraph in) it allows together graph T such that T is a tree, in other words if there is a tree such that each hyper-edge H induces a substructure in T.

Since a tree is a tree hyper hyper trees can be seen as a generalization of the concept of a tree for hypergraphs. Each hyper tree is isomorphic with some family members of substructures of a tree.

**Characteristics: –**

A hyper tree Helly the characteristic (2-Helly property), that is to say, if two hyperedges of a subset of the hyperedges a common vertex, then all hyperedges of the subset have a common vertex.

The results of Duchet, Flament and Slater (see for example), a hypergraph is a hyper tree if and only if it has the Helly property and the line graph is chordal if and only if the dual hypergraph is compliant and chordal.

So a hypergraph a hyper tree if and only if the dual hypergraph alpha-acyclic (within the meaning of Fagin et al.)

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