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    <div id="titlebar">Graph Theory: Industrial Drilling</div>
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			Home &gt; Graph Theory: Industrial Drilling
					&gt; Solving the Drilling Problem
					&gt; Independent Sets, Cliques, etc.</div>
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        <a class="toc_link" href="page1.xml">The Drilling Problem</a>
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        <a class="toc_link" href="">Solving the Drilling Problem</a>
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        <a class="toc_link" href="page24.xml">Independent Sets, Cliques, etc.</a>
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        <a class="toc_link" href="page26.xml">Vertex Coloring</a>
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        <a class="toc_link" href="page31.xml">First Lower Bound</a>
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        <a class="toc_link" href="page33.xml">The Inside View</a>
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    <div id="content"><h1>Independent Sets, Cliques, etc.</h1>
				<ol><li>
					A set of vertices is called <i>independent</i> 
					if no two vertices in the set are adjacent.
					</li><li>
					A set of vertices is called a <i>clique</i> 
					if every pair of vertices in the set is adjacent.
					</li><li>
					An independent set (resp. a clique) is called <i>maximal</i> 
					if no other independent set (resp. clique) contains it.
					</li><li>
					An independent set (resp. a clique) is called <i>maximum</i> 
					if its cardinality is maximal among all independent sets (resp. clique) in the graph.
					</li><li>
					<m:math><m:mi>α</m:mi><m:mfenced><m:mi>G</m:mi></m:mfenced></m:math> (resp.
					<m:math><m:mi>ω</m:mi><m:mfenced><m:mi>G</m:mi></m:mfenced></m:math>) 
					denotes the maximum size of an independent set (resp. a clique) in a graph <m:math><m:mi>G</m:mi></m:math>.
					</li><li>
					A set of edges in a graph is called a <i>matching</i> 
					if no two of them are incident to the same vertex. 
					<m:math><m:mi>π</m:mi><m:mfenced><m:mi>G</m:mi></m:mfenced></m:math> denotes the maximum size of a matching in a graph <m:math><m:mi>G</m:mi></m:math>.
					</li></ol>
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