Open Problem Garden - Negative association in uniform forests - Comments

Open Problem Garden - Negative association in uniform forests - Comments http://openproblemgarden.org/op/negative_association_in_uniform_forests Comments for "Negative association in uniform forests" en Negative association in uniform forests http://openproblemgarden.org/op/negative_association_in_uniform_forests <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/pemantle_robin">Pemantle</a>   </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/random_graphs">Probabilistic G.T.</a>   </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>   Let <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> be a finite graph, let <img class="teximage" src="/files/tex/785dc08a907b3bfba9d96f51396e90572dfbc853.png" alt="$ e,f \in E(G) $" />, and let <img class="teximage" src="/files/tex/bfff269cc7df9bdb7c57d8b6a2a74020d114f24d.png" alt="$ F $" /> be the edge set of a forest chosen uniformly at random from all forests of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />. Then <img class="teximage" src="/files/tex/1fe7ac9c579238670e3aa16ae401e8194e1c3da3.png" alt="\[ {\mathbb P}(e \in F \mid f \in F}) \le {\mathbb P}(e \in F) \]" /> </div> </tr></td> </table> </td> </tr> </table> Pemantle, Robin forest negative association Graph Theory Probabilistic Graph Theory http://openproblemgarden.org/op/negative_association_in_uniform_forests#comment Mon, 30 Jun 2008 13:36:49 +0200 mdevos 1757 at http://openproblemgarden.org