http://openproblemgarden.org/op/monochromatoc_reachability_in_arc_colored_digraphs Comments for "Monochromatic reachability in arc-colored digraphs" en http://openproblemgarden.org/op/monochromatoc_reachability_in_arc_colored_digraphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/sands_bill">Sands</a>; <a href="/category/sauer_norbert_w">Sauer</a>; <a href="/category/woodrow_robert_e">Woodrow</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; For every <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />, there exists an integer <img class="teximage" src="/files/tex/e055b3867e7cb3cc4b2f50739eedda7657999214.png" alt="$ f(k) $" /> such that if <img class="teximage" src="/files/tex/b8653a25aff72e3dacd3642492c24c2241f0058c.png" alt="$ D $" /> is a digraph whose arcs are colored with <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" /> colors, then <img class="teximage" src="/files/tex/b8653a25aff72e3dacd3642492c24c2241f0058c.png" alt="$ D $" /> has a <img class="teximage" src="/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png" alt="$ S $" /> set which is the union of <img class="teximage" src="/files/tex/e055b3867e7cb3cc4b2f50739eedda7657999214.png" alt="$ f(k) $" /> stables sets so that every vertex has a monochromatic path to some vertex in <img class="teximage" src="/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png" alt="$ S $" />. </div> </tr></td> </table> </td> </tr> </table> Sands, Bill Sauer, Norbert W. Woodrow, Robert E. Graph Theory Directed Graphs http://openproblemgarden.org/op/monochromatoc_reachability_in_arc_colored_digraphs#comment Tue, 04 Apr 2017 22:56:57 +0200 fhavet 60028 at http://openproblemgarden.org