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<head><title>isChordal -- determines if a graph is chordal</title>
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<div><h1>isChordal -- determines if a graph is chordal</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 = isChordal 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 the graph is chordal</span></li>
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<div class="single"><h2>Description</h2>
<div><div>A graph is chordal if the graph has no induced cycles of length 4 or more (triangles are allowed). To check if a graph is chordal, we use a characterization of Fröberg (see "On Stanley-Reisner rings," Topics in algebra, Part 2 (Warsaw, 1988), 57-70, Banach Center Publ., 26, Part 2, PWN, Warsaw, 1990.) that says that a graph G is chordal if and only if the edge ideal of G<sup>c</sup> has a linear resolution, where G<sup>c</sup> is the complementary graph of G.</div>
<table class="examples"><tr><td><pre>i1 : S = QQ[a..e];</pre>
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<tr><td><pre>i2 : C = cycle S;</pre>
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<tr><td><pre>i3 : isChordal C
o3 = false</pre>
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<tr><td><pre>i4 : D = graph {a*b,b*c,c*d,a*c};</pre>
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<tr><td><pre>i5 : isChordal D
o5 = true</pre>
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<tr><td><pre>i6 : E = completeGraph S;</pre>
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<tr><td><pre>i7 : isChordal E
o7 = true</pre>
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<div class="waystouse"><h2>Ways to use <tt>isChordal</tt> :</h2>
<ul><li>isChordal(Graph)</li>
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