http://www.openproblemgarden.org/op/bigger_cycles_in_cubic_graphs Comments for "Bigger cycles in cubic graphs" en http://www.openproblemgarden.org/op/bigger_cycles_in_cubic_graphs#comment-6661 <p>In the paper "Stable dominating circuits in snarks" (Discrete Math 233 (247-256) 2001) Martin Kochhol gives a counter example to this conjecture (in fact he gives an infinite family of them). </p> <p>Using computer search I have found even smaller counter examples (the smallest has just 20 vertices).</p> <p>Best regards,</p> <p>Jonas Hägglund</p> Fri, 04 Sep 2009 14:16:41 +0200 Anonymous comment 6661 at http://www.openproblemgarden.org http://www.openproblemgarden.org/op/bigger_cycles_in_cubic_graphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/basic_graph_theory">Basic G.T.</a> » <a href="/category/cycles_0">Cycles</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Problem</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> be a cyclically 4-edge-connected cubic graph and let <img class="teximage" src="/files/tex/05d3558ef52267cc1af40e658352d98883668ee3.png" alt="$ C $" /> be a cycle of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />. Must there exist a cycle <img class="teximage" src="/files/tex/c3199a0094ee88c4571a3a65defc88a4343532ca.png" alt="$ C&#039; \neq C $" /> so that <img class="teximage" src="/files/tex/e5b68d14640cffba06d035388ad1465bb885f72e.png" alt="$ V(C) \subseteq V(C&#039;) $" />? </div> </tr></td> </table> </td> </tr> </table> cubic cycle Graph Theory Basic Graph Theory Cycles http://www.openproblemgarden.org/op/bigger_cycles_in_cubic_graphs#comment Fri, 31 Aug 2007 08:25:16 +0200 mdevos 546 at http://www.openproblemgarden.org