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<head><title>isGoodLeaf -- determines if an edge is a good leaf</title>
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<div><h1>isGoodLeaf -- determines if an edge 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>b = isGoodLeaf(H,n)</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>
<li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, index of an edge</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>b</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <tt>true</tt> if edge <tt>n</tt> of <tt>H</tt> is a good leaf</span></li>
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<div class="single"><h2>Description</h2>
<div><div>A good leaf of 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. 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 : edges(H)
o3 = {{a, b, c, d}, {b, c, d, e}, {c, d, f}, {d, g}, {e, f, g}}
o3 : List</pre>
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<tr><td><pre>i4 : isGoodLeaf(H,0)
o4 = true</pre>
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<tr><td><pre>i5 : isGoodLeaf(H,1)
o5 = false</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_get__Good__Leaf.html" title="returns an edge that is a good leaf">getGoodLeaf</a> -- returns an edge that is a good leaf</span></li>
<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>
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<div class="waystouse"><h2>Ways to use <tt>isGoodLeaf</tt> :</h2>
<ul><li>isGoodLeaf(HyperGraph,ZZ)</li>
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