http://openproblemgarden.org/op/kriesells_conjecture Comments for "Kriesell's Conjecture" en http://openproblemgarden.org/op/kriesells_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/kriesell_matthias">Kriesell</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/basic_graph_theory">Basic G.T.</a> » <a href="/category/connectivity">Connectivity</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/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> be a graph and let <img class="teximage" src="/files/tex/0acf1a8ecf3a0737d34c34b8652d10a2c33df19b.png" alt="$ T\subseteq V(G) $" /> such that for any pair <img class="teximage" src="/files/tex/bbcef09f86563651f02daa6bbae826055f48edfb.png" alt="$ u,v\in T $" /> there are <img class="teximage" src="/files/tex/bded1a5bf39ed2baaf98bd8c04cea4667dd89b58.png" alt="$ 2k $" /> edge-disjoint paths from <img class="teximage" src="/files/tex/06183efdad837019eb0937c4e40f9e7beaa2e8d8.png" alt="$ u $" /> to <img class="teximage" src="/files/tex/96cbd9a16c6a5eab03815b093b08f3b2db614e9a.png" alt="$ v $" /> in <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />. Then <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> contains <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" /> edge-disjoint trees, each of which contains <img class="teximage" src="/files/tex/79f55d2e1d83a7726c807a70cbe756713b0437b6.png" alt="$ T $" />. </div> </tr></td> </table> </td> </tr> </table> Kriesell, Matthias Disjoint paths edge-connectivity spanning trees Graph Theory Basic Graph Theory Connectivity http://openproblemgarden.org/op/kriesells_conjecture#comment Sun, 25 Aug 2013 21:32:22 +0200 Jon Noel 56233 at http://openproblemgarden.org