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<head><title>cliqueNumber -- computes the clique number of a graph</title>
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<div><h1>cliqueNumber -- computes the clique number of a graph</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>c = cliqueNumber 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>c</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the clique number of <tt>G</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><div>cliqueNumber returns the clique number of a graph, the size of the largest clique contained in the graph. This number is also related to the dimension of the clique complex of the graph.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : cliqueNumber completeGraph R
o2 = 4</pre>
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<tr><td><pre>i3 : G = graph({a*b,b*c,a*c,a*d})
o3 = Graph{edges => {{a, b}, {a, c}, {b, c}, {a, d}}}
ring => R
vertices => {a, b, c, d}
o3 : Graph</pre>
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<tr><td><pre>i4 : cliqueNumber G
o4 = 3</pre>
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<tr><td><pre>i5 : dim cliqueComplex G + 1 == cliqueNumber G
o5 = true</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_clique__Complex.html" title="returns the clique complex of a graph">cliqueComplex</a> -- returns the clique complex of a graph</span></li>
<li><span><a href="_get__Cliques.html" title="returns cliques in a graph">getCliques</a> -- returns cliques in a graph</span></li>
<li><span><a href="_get__Max__Cliques.html" title="returns maximal cliques in a graph">getMaxCliques</a> -- returns maximal cliques in a graph</span></li>
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<div class="waystouse"><h2>Ways to use <tt>cliqueNumber</tt> :</h2>
<ul><li>cliqueNumber(Graph)</li>
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