http://openproblemgarden.org/op/monochromatic_reachability_in_edge_colored_digraphs Comments for "Monochromatic reachability in edge-colored tournaments" en http://openproblemgarden.org/op/monochromatic_reachability_in_edge_colored_digraphs <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/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; For every <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" />, is there a (least) positive integer <img class="teximage" src="/files/tex/9579fe06c51fc31a993cd148e8bbc3cb07df464e.png" alt="$ f(n) $" /> so that whenever a tournament has its edges colored with <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> colors, there exists a set <img class="teximage" src="/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png" alt="$ S $" /> of at most <img class="teximage" src="/files/tex/9579fe06c51fc31a993cd148e8bbc3cb07df464e.png" alt="$ f(n) $" /> vertices so that every vertex has a monochromatic path to some point in <img class="teximage" src="/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png" alt="$ S $" />? </div> </tr></td> </table> </td> </tr> </table> Erdos, Paul digraph edge-coloring tournament Graph Theory Directed Graphs Tournaments http://openproblemgarden.org/op/monochromatic_reachability_in_edge_colored_digraphs#comment Wed, 09 Jul 2008 22:46:42 +0200 mdevos 1801 at http://openproblemgarden.org