Open Problem Garden - Partitionning a tournament into k-strongly connected subtournaments. - Comments http://openproblemgarden.org/op/partitionning_a_tournament_into_k_strongly_connected_subtournaments Comments for "Partitionning a tournament into k-strongly connected subtournaments." en Partitionning a tournament into k-strongly connected subtournaments. http://openproblemgarden.org/op/partitionning_a_tournament_into_k_strongly_connected_subtournaments <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/directed_graphs">Directed Graphs</a> » <a href="/category/tournaments">Tournaments</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Problem</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/dd32073e76a3e937a33f354d483a622b518fd952.png" alt="$ k_1, \dots , k_p $" /> be positve integer Does there exists an integer <img class="teximage" src="/files/tex/d421e344ef4e58f862c849a1510c5bfbc987695c.png" alt="$ g(k_1, \dots , k_p) $" /> such that every <img class="teximage" src="/files/tex/d421e344ef4e58f862c849a1510c5bfbc987695c.png" alt="$ g(k_1, \dots , k_p) $" />-strong tournament <img class="teximage" src="/files/tex/79f55d2e1d83a7726c807a70cbe756713b0437b6.png" alt="$ T $" /> admits a partition <img class="teximage" src="/files/tex/5a9d8fc043fbbf884f7a132e075c21bcfc070b50.png" alt="$ (V_1\dots , V_p) $" /> of its vertex set such that the subtournament induced by <img class="teximage" src="/files/tex/af854be1f03aac481e0a165c3908976d4b5b0aa0.png" alt="$ V_i $" /> is a non-trivial <img class="teximage" src="/files/tex/e4854627e64b06bb06bbeb46f57f3b1e9b30b1b7.png" alt="$ k_i $" />-strong for all <img class="teximage" src="/files/tex/4e9f329cd88669519e011cd4cd2fb9a90b5b4828.png" alt="$ 1\leq i\leq p $" />. </div> </tr></td> </table> </td> </tr> </table> Thomassen, Carsten Graph Theory Directed Graphs Tournaments http://openproblemgarden.org/op/partitionning_a_tournament_into_k_strongly_connected_subtournaments#comment Fri, 15 Mar 2013 04:52:04 +0100 fhavet 47643 at http://openproblemgarden.org