http://openproblemgarden.org/op/dings_tau_r_vs_tau_conjecture Comments for "Ding's tau_r vs. tau conjecture" en http://openproblemgarden.org/op/dings_tau_r_vs_tau_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/ding_guoli">Ding</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/combinatorics">Combinatorics</a> » <a href="/category/optimization">Optimization</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/44f910a811a9d2212e22c6bd7fabe7de0bd5e7fe.png" alt="$ r \ge 2 $" /> be an integer and let <img class="teximage" src="/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png" alt="$ H $" /> be a minor minimal <a href="http://en.wikipedia.org/wiki/clutter">clutter</a> with <img class="teximage" src="/files/tex/b886bbe2e88e54cd298fbc37bbbe43ea9b09c9b7.png" alt="$ \frac{1}{r}\tau_r(H) &lt; \tau(H) $" />. Then either <img class="teximage" src="/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png" alt="$ H $" /> has a <img class="teximage" src="/files/tex/ba650479e114120ba9553d070affc34746d309b2.png" alt="$ J_k $" /> minor for some <img class="teximage" src="/files/tex/1fb800e3b693294681248f4481b3c041cdcaf1d3.png" alt="$ k \ge 2 $" /> or <img class="teximage" src="/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png" alt="$ H $" /> has Lehman's property. </div> </tr></td> </table> </td> </tr> </table> Ding, Guoli clutter covering MFMC property packing Combinatorics Optimization http://openproblemgarden.org/op/dings_tau_r_vs_tau_conjecture#comment Sun, 11 Nov 2007 04:32:26 +0100 mdevos 696 at http://openproblemgarden.org