http://openproblemgarden.org/op/frankls_union_closed_sets_conjecture Comments for "Frankl's union-closed sets conjecture" en http://openproblemgarden.org/op/frankls_union_closed_sets_conjecture#comment-6698 <p>Does anyone know if there is any linear bound known instead of 1/2?</p> Thu, 17 Dec 2009 11:59:43 +0100 Anonymous comment 6698 at http://openproblemgarden.org http://openproblemgarden.org/op/frankls_union_closed_sets_conjecture#comment-6621 <p>For mor einformation and many references see also West's account in: http://www.math.uiuc.edu/~west/openp/unionclos.html</p> Sat, 07 Mar 2009 09:19:25 +0100 Anonymous comment 6621 at http://openproblemgarden.org http://openproblemgarden.org/op/frankls_union_closed_sets_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/frankl_peter">Frankl</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/hypergraphs">Hypergraphs</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/bfff269cc7df9bdb7c57d8b6a2a74020d114f24d.png" alt="$ F $" /> be a finite family of finite sets, not all empty, that is closed under taking unions. Then there exists <img class="teximage" src="/files/tex/e7ba5befcaa0d78e43b5176d70ce67425fd0fcdc.png" alt="$ x $" /> such that <img class="teximage" src="/files/tex/e7ba5befcaa0d78e43b5176d70ce67425fd0fcdc.png" alt="$ x $" /> is an element of at least half the members of <img class="teximage" src="/files/tex/bfff269cc7df9bdb7c57d8b6a2a74020d114f24d.png" alt="$ F $" />. </div> </tr></td> </table> </td> </tr> </table> Frankl, Peter Graph Theory Hypergraphs http://openproblemgarden.org/op/frankls_union_closed_sets_conjecture#comment Thu, 25 Sep 2008 17:18:02 +0200 tchow 2108 at http://openproblemgarden.org