http://openproblemgarden.org/op/hamilton_cycle_in_small_d_diregular_graphs Comments for "Hamilton cycle in small d-diregular graphs" en http://openproblemgarden.org/op/hamilton_cycle_in_small_d_diregular_graphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/jackson_bill">Jackson</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/directed_graphs">Directed Graphs</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>An directed graph is <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-diregular if every vertex has indegree and outdegree at least <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />.</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; For <img class="teximage" src="/files/tex/6b29cd29e21416ff46f4898a33bcc7355436ee8f.png" alt="$ d &gt;2 $" />, every <img class="teximage" src="/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png" alt="$ d $" />-diregular oriented graph on at most <img class="teximage" src="/files/tex/5d467147b18bddde059e7178ebf5bcf6c4b4f516.png" alt="$ 4d+1 $" /> vertices has a Hamilton cycle. </div> </tr></td> </table> </td> </tr> </table> Jackson, Bill Graph Theory Directed Graphs http://openproblemgarden.org/op/hamilton_cycle_in_small_d_diregular_graphs#comment Fri, 08 Mar 2013 05:32:25 +0100 fhavet 47028 at http://openproblemgarden.org