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# hasGoodLeaf -- determines if a HyperGraph contains a good leaf

- Usage:
    `b = hasGoodLeaf(H)`
- Inputs:
  - H, a hypergraph,
- Outputs:
  - b, a Boolean value, true if H contains an edge that is a good leaf

## Description

A good leaf of hypergraph H is an edge L whose intersections with all other edges form a totally ordered set. It follows that L must have a free vertex. In the graph setting, a good leaf is an edge containing a vertex of degree one. The notion of a good leaf was introduced by X. Zheng in her Ph.D. thesis (2004).

    i1 : R = QQ[a..g];

    i2 : H = hyperGraph {b*c*d*e, a*b*c*d, c*d*f, d*g, e*f*g};

    i3 : hasGoodLeaf(H)

    o3 = true

    i4 : getGoodLeaf(H)

    o4 = {a, b, c, d}

    o4 : List

## See also

- getGoodLeaf -- returns an edge that is a good leaf
- getGoodLeafIndex -- returns the index of an edge that is a good leaf
- isGoodLeaf -- determines if an edge is a good leaf

## Ways to use hasGoodLeaf:

- `hasGoodLeaf(HyperGraph)`

## For the programmer

The object hasGoodLeaf is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/EdgeIdeals.m2:2768:0.