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<head><title>getGoodLeaf -- returns an edge that is a good leaf</title>
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<div><h1>getGoodLeaf -- returns an edge that is a good leaf</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>L = getGoodLeaf(H)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>H</tt>, <span>a <a href="___Hyper__Graph.html">hypergraph</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of vertices that comprise an edge in H that is a good leaf</span></li>
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<div class="single"><h2>Description</h2>
<div><div>A good leaf of a hypergraph <tt>H</tt> is an edge <tt>L</tt> whose intersections with all other edges form a totally ordered set. It follows that <tt>L</tt> 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).</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a..g];</pre>
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<tr><td><pre>i2 : H = hyperGraph {a*b*c*d, b*c*d*e, c*d*f, d*g, e*f*g};</pre>
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<tr><td><pre>i3 : getGoodLeaf(H)
o3 = {a, b, c, d}
o3 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_get__Good__Leaf__Index.html" title="returns the index of an edge that is a good leaf">getGoodLeafIndex</a> -- returns the index of an edge that is a good leaf</span></li>
<li><span><a href="_has__Good__Leaf.html" title="determines if a HyperGraph contains a good leaf">hasGoodLeaf</a> -- determines if a HyperGraph contains a good leaf</span></li>
<li><span><a href="_is__Good__Leaf.html" title="determines if an edge is a good leaf">isGoodLeaf</a> -- determines if an edge is a good leaf</span></li>
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<div class="waystouse"><h2>Ways to use <tt>getGoodLeaf</tt> :</h2>
<ul><li>getGoodLeaf(HyperGraph)</li>
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