hamilcyc.html

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<TITLE>Hamiltonian cycle</TITLE>
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  content="Definition of Hamiltonian cycle,
	possibly with links to more information and implementations.">
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<H1>Hamiltonian cycle</H1>
<P>
(definition)

<P>
<strong>Definition:</strong>
A <a href="path.html" tppabs="http://hissa.nist.gov/dads/HTML/path.html"><em>path</em></a> through a <a href="graph.html" tppabs="http://hissa.nist.gov/dads/HTML/graph.html"><em>graph</em></a> which starts and ends at the same <a href="vertex.html" tppabs="http://hissa.nist.gov/dads/HTML/vertex.html"><em>vertex</em></a> and includes every other vertex exactly once.  Also known as a <em>tour</em>.
<P><strong>See also</strong>
<a href="cycle.html" tppabs="http://hissa.nist.gov/dads/HTML/cycle.html"><em>cycle</em></a>, <a href="travelsales.html" tppabs="http://hissa.nist.gov/dads/HTML/travelsales.html"><em>traveling salesman</em></a>, <a href="eulercycle.html" tppabs="http://hissa.nist.gov/dads/HTML/eulercycle.html"><em>Euler cycle</em></a>.
<P><em>Note:
Named for W. R. Hamilton (from J. A. Bondy and U. S. R. Murty. <em>Graph Theory with Applications</em>.  1976) A Hamiltonian cycle includes each vertex once; an Euler cycle includes each edge once.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>
<H2>Implementation</H2>
<A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.sunysb.edu/%7Ealgorith/files/hamiltonian-cycle.shtml  \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://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.sunysb.edu/%7Ealgorith/files/hamiltonian-cycle.shtml'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.sunysb.edu/%7Ealgorith/files/hamiltonian-cycle.shtml">(Fortran, C, Mathematica, and C++)</A>

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Go to the
<A HREF="terms.html" tppabs="http://hissa.nist.gov/dads/terms.html">Algorithms, Data Structures, and Problems</A>
home page.

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If you have suggestions, corrections, or comments, please get in touch
with
<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>
&nbsp;(<a href="mailto:paul.black@nist.gov">paul.black@nist.gov</a>).

<p>
Entry modified Thu Mar 18 08:30:54 1999.<BR>
HTML page formatted Wed Dec 22 09:35:28 1999.

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