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<head><title>isPerfect -- determines whether a graph is perfect</title>
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<div><h1>isPerfect -- determines whether a graph is perfect</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 = isPerfect G</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>G</tt>, <span>a <a href="___Graph.html">graph</a></span></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 <tt>G</tt> is perfect and <tt>false</tt> otherwise</span></li>
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<div class="single"><h2>Description</h2>
<div><div>The algorithm uses the Strong Perfect Graph Theorem, which says that <tt>G</tt> is perfect if and only if neither <tt>G</tt> nor its complement contains an odd hole. <a href="_has__Odd__Hole.html" title="tells whether a graph contains an odd hole">hasOddHole</a> is used to determine whether these conditions hold.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[x_1..x_7];</pre>
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<tr><td><pre>i2 : G = complementGraph cycle R; --odd antihole with 7 vertices</pre>
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<tr><td><pre>i3 : isPerfect G
o3 = false</pre>
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<tr><td><pre>i4 : H = cycle(R,4)
o4 = Graph{edges => {{x , x }, {x , x }, {x , x }, {x , x }}}
1 2 2 3 3 4 1 4
ring => R
vertices => {x , x , x , x , x , x , x }
1 2 3 4 5 6 7
o4 : Graph</pre>
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<tr><td><pre>i5 : isPerfect H
o5 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_has__Odd__Hole.html" title="tells whether a graph contains an odd hole">hasOddHole</a> -- tells whether a graph contains an odd hole</span></li>
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<div class="waystouse"><h2>Ways to use <tt>isPerfect</tt> :</h2>
<ul><li>isPerfect(Graph)</li>
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