http://openproblemgarden.org/op/subgraph_of_large_average_degree_and_large_average_degree Comments for "Subgraph of large average degree and large girth." en http://openproblemgarden.org/op/subgraph_of_large_average_degree_and_large_average_degree <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/thomassen_carsten">Thomassen</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>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; For all positive integers <img class="teximage" src="/files/tex/4239ee4145983e1d8ad375f0606cc7140bce36a3.png" alt="$ g $" /> and <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />, there exists an integer <img class="teximage" src="/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png" alt="$ d $" /> such that every graph of average degree at least <img class="teximage" src="/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png" alt="$ d $" /> contains a subgraph of average degree at least <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" /> and girth greater than <img class="teximage" src="/files/tex/4239ee4145983e1d8ad375f0606cc7140bce36a3.png" alt="$ g $" />. </div> </tr></td> </table> </td> </tr> </table> Thomassen, Carsten Graph Theory Basic Graph Theory http://openproblemgarden.org/op/subgraph_of_large_average_degree_and_large_average_degree#comment Tue, 05 Mar 2013 02:53:51 +0100 fhavet 46708 at http://openproblemgarden.org