http://openproblemgarden.org/op/packing_t_joins Comments for "Packing T-joins" en http://openproblemgarden.org/op/packing_t_joins <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/devos">DeVos</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/coloring">Coloring</a> » <a href="/category/edge_coloring">Edge coloring</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 $" /> (probably <img class="teximage" src="/files/tex/7a8b9609d823e7ffb81159e3dfcbd5cb2599e11d.png" alt="$ c=1 $" /> suffices) so that every graft with minimum <img class="teximage" src="/files/tex/79f55d2e1d83a7726c807a70cbe756713b0437b6.png" alt="$ T $" />-cut size at least <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" /> contains a <img class="teximage" src="/files/tex/79f55d2e1d83a7726c807a70cbe756713b0437b6.png" alt="$ T $" />-join packing of size at least <img class="teximage" src="/files/tex/da50fbb1472ce7fd6fa00876af3022e1be50d2ec.png" alt="$ (2/3)k-c $" />. </div> </tr></td> </table> </td> </tr> </table> DeVos, Matt packing T-join Graph Theory Coloring Edge coloring http://openproblemgarden.org/op/packing_t_joins#comment Wed, 07 Mar 2007 14:27:18 +0100 mdevos 144 at http://openproblemgarden.org