http://openproblemgarden.org/op/exponentially_many_perfect_matchings_in_cubic_graphs Comments for "Exponentially many perfect matchings in cubic graphs" en http://openproblemgarden.org/op/exponentially_many_perfect_matchings_in_cubic_graphs#comment-6878 <p>The paper is now available in preprint form on arXiv. http://arxiv.org/abs/1012.2878</p> Wed, 15 Dec 2010 21:09:21 +0100 Andrew King comment 6878 at http://openproblemgarden.org http://openproblemgarden.org/op/exponentially_many_perfect_matchings_in_cubic_graphs#comment-6857 <p>The conjecture has recently been proven by Esperet, Kardos, King, Kral and Norine. The paper is now being prepared for publication.</p> Mon, 08 Nov 2010 22:25:03 +0100 Anonymous comment 6857 at http://openproblemgarden.org http://openproblemgarden.org/op/exponentially_many_perfect_matchings_in_cubic_graphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/lovasz">Lovasz</a>; <a href="/category/plummer_michael_d">Plummer</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/matchings_0">Matchings</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; There exists a fixed constant <img class="teximage" src="/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png" alt="$ c $" /> so that every <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" />-vertex cubic graph without a cut-edge has at least <img class="teximage" src="/files/tex/22656fabb8498ada6bf54e6068c4978436afcc8f.png" alt="$ e^{cn} $" /> perfect matchings. </div> </tr></td> </table> </td> </tr> </table> Lovasz, Laszlo Plummer, Michael D. cubic perfect matching Graph Theory Basic Graph Theory Matchings http://openproblemgarden.org/op/exponentially_many_perfect_matchings_in_cubic_graphs#comment Mon, 30 Jun 2008 12:39:54 +0200 mdevos 1755 at http://openproblemgarden.org