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possibly with links to more information and implementations.">
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<H1>perfect matching</H1>
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(definition)
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<strong>Definition:</strong>
A <a href="matching.html" tppabs="http://hissa.nist.gov/dads/HTML/matching.html"><em>matching</em></a>, or subset of <a href="edge.html" tppabs="http://hissa.nist.gov/dads/HTML/edge.html"><em>edges</em></a> without common <a href="vertex.html" tppabs="http://hissa.nist.gov/dads/HTML/vertex.html"><em>vertices</em></a>, of a <a href="connectdgraf.html" tppabs="http://hissa.nist.gov/dads/HTML/connectdgraf.html"><em>connected graph</em></a> which touch all vertices exactly once. A graph with an odd number of vertices has one unmatched vertex.
<P><em>Note:
Since an <a href="undirectgraf.html" tppabs="http://hissa.nist.gov/dads/HTML/undirectgraf.html"><em>undirected</em></a> connected graph without <a href="selfloop.html" tppabs="http://hissa.nist.gov/dads/HTML/selfloop.html"><em>self-loops</em></a> has n(n-1)/2 edges, where n is the number of vertices, a perfect match consists of n/2 of the edges. The name of the term comes from matching each vertex with exactly one other vertex.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>
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Go to the
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<a href="javascript:if(confirm('http://hissa.nist.gov/~black/black.html \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://hissa.nist.gov/~black/black.html'" tppabs="http://hissa.nist.gov/~black/black.html">Paul E. Black</a>
(<a href="mailto:paul.black@nist.gov">paul.black@nist.gov</a>).
<p>
Entry modified Fri Jul 23 12:39:51 1999.<BR>
HTML page formatted Wed Dec 22 09:36:08 1999.
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