http://openproblemgarden.org/op/simultaneous_partition_of_hypergraphs Comments for "Simultaneous partition of hypergraphs" en http://openproblemgarden.org/op/simultaneous_partition_of_hypergraphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/kuhn_daniella">Kühn</a>; <a href="/category/osthus_deryk">Osthus</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>Problem</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/eb41970b0531bb084fea9f6967da01b53f441664.png" alt="$ H_1 $" /> and <img class="teximage" src="/files/tex/2d70749ca9db234020c5071434ce58006623b919.png" alt="$ H_2 $" /> be two <img class="teximage" src="/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png" alt="$ r $" />-uniform hypergraph on the same vertex set <img class="teximage" src="/files/tex/517af4139f21bb21424f7896561555919bc4678a.png" alt="$ V $" />. Does there always exist a partition of <img class="teximage" src="/files/tex/517af4139f21bb21424f7896561555919bc4678a.png" alt="$ V $" /> into <img class="teximage" src="/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png" alt="$ r $" /> classes <img class="teximage" src="/files/tex/9840205fdc1959213e766b6ed6ddd1dd952dc228.png" alt="$ V_1, \dots , V_r $" /> such that for both <img class="teximage" src="/files/tex/1db9f0079a9ca23741381d2fbc830c48d730c458.png" alt="$ i=1,2 $" />, at least <img class="teximage" src="/files/tex/d65114aa913d6d3c960fc0fff99b77050111639d.png" alt="$ r!m_i/r^r -o(m_i) $" /> hyperedges of <img class="teximage" src="/files/tex/b5eebbb6562e3e98766f53decb43a78b1f076151.png" alt="$ H_i $" /> meet each of the classes <img class="teximage" src="/files/tex/9840205fdc1959213e766b6ed6ddd1dd952dc228.png" alt="$ V_1, \dots , V_r $" />? </div> </tr></td> </table> </td> </tr> </table> Kühn, Daniella Osthus, Deryk Graph Theory Hypergraphs http://openproblemgarden.org/op/simultaneous_partition_of_hypergraphs#comment Wed, 06 Mar 2013 03:56:31 +0100 fhavet 46817 at http://openproblemgarden.org