Thinking about this further last night, I can refine the requirement to finding: that union of cyclic alternating paths which puts each node in the longest possible cycle. This page you referenced uses the discovery of alternating paths at the core of its algorithm - I need to analyse it further to see if it can be extended to discern the longest cycles.
I was perhaps overly swayed by reading that the problem of "finding the longest cycle" is NP-hard - that is for a general graph, and it seems entirely possible that the special case of a bipartite graph introduces enough structure to make it rather easier.
Are you posting in the right place? Check out Where do I post X? to know for sure.
Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
<code> <a> <b> <big>
<blockquote> <br /> <dd>
<dl> <dt> <em> <font>
<h1> <h2> <h3> <h4>
<h5> <h6> <hr /> <i>
<li> <nbsp> <ol> <p>
<small> <strike> <strong>
<sub> <sup> <table>
<td> <th> <tr> <tt>
Snippets of code should be wrapped in
<code> tags not
<pre> tags. In fact, <pre>
tags should generally be avoided. If they must
be used, extreme care should be
taken to ensure that their contents do not
have long lines (<70 chars), in order to prevent
horizontal scrolling (and possible janitor
Want more info? How to link or
or How to display code and escape characters
are good places to start.