A good leaf of a 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, i.e., a vertex contained in no other edges. 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 {a*b*c*d, b*c*d*e, c*d*f, d*g, e*f*g};
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i3 : getGoodLeaf(H)
o3 = {a, b, c, d}
o3 : List
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The object getGoodLeaf is a method function.