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POPalmer's Algorithm for Hamiltonian cycles
 

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    <p>In a "dense" graph, I am trying to construct a Hamiltonian cycle using <a href="http://en.wikipedia.org/wiki/Ore%27s_theorem" rel="nofollow">Palmer's Algorithm</a>. However, I need more explanation for this algorithm because it does not work with me when I implement it. It seems that there is an unclear part in Wikipedia's explanation. </p> <p>I would be thankful if someone explains it more clearly or give me some links to read. </p> <p>Here's the algorithm statement:</p> <blockquote> <p>Palmer (1997) describes the following simple algorithm for constructing a Hamiltonian cycle in a graph meeting Ore's condition. Arrange the vertices arbitrarily into a cycle, ignoring adjacencies in the graph. While the cycle contains two consecutive vertices <code>vi</code> and <code>vi + 1</code> that are not adjacent in the graph, perform the following two steps:</p> <ul> <li><p>Search for an index <code>j</code> such that the four vertices <code>vi</code>, <code>vi + 1</code>, <code>vj</code>, and <code>vj + 1</code> are all distinct and such that the graph contains edges from <code>vi</code> to <code>vj + 1</code> and from <code>vj</code> to <code>vi + 1</code></p></li> <li><p>Reverse the part of the cycle between <code>vi + 1</code> and <code>vj</code> (inclusive).</p></li> </ul> </blockquote> <p>To be more specific, I do not get the part where they say: "Arrange the vertices arbitrarily into a cycle" in this case, is this right to do: 0,1,2,3,4,0</p> <p>and what do they mean by: "Reverse the part of the cycle"?</p>
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