http://openproblemgarden.org/op/partitioning_planar_digraphs Comments for "The Two Color Conjecture" en http://openproblemgarden.org/op/partitioning_planar_digraphs#comment-18 <p>Riste Skrekovski conjectured at a graph theory meeting in Budmerice, Slovakia, in 2005 that this conjecture is false.</p> Thu, 31 May 2007 02:23:13 +0200 Anonymous comment 18 at http://openproblemgarden.org http://openproblemgarden.org/op/partitioning_planar_digraphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/neumann_lara_victor">Neumann-Lara</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/directed_graphs">Directed Graphs</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; If <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is an orientation of a simple planar graph, then there is a partition of <img class="teximage" src="/files/tex/b324b54d8674fa66eb7e616b03c7a601ccdab6b8.png" alt="$ V(G) $" /> into <img class="teximage" src="/files/tex/1ac50179d3c46ba43d2b8183a945de84c223f351.png" alt="$ \{X_1,X_2\} $" /> so that the graph induced by <img class="teximage" src="/files/tex/4d0fffaf276df9eeca81fca1efb9e42157b0a9f9.png" alt="$ X_i $" /> is acyclic for <img class="teximage" src="/files/tex/1db9f0079a9ca23741381d2fbc830c48d730c458.png" alt="$ i=1,2 $" />. </div> </tr></td> </table> </td> </tr> </table> Neumann-Lara, Victor acyclic digraph planar Graph Theory Directed Graphs http://openproblemgarden.org/op/partitioning_planar_digraphs#comment Mon, 26 Mar 2007 15:15:38 +0200 mdevos 169 at http://openproblemgarden.org