http://openproblemgarden.org/op/choice_number_of_k_chromatic_graphs_of_bounded_order Comments for "Choice Number of k-Chromatic Graphs of Bounded Order" en http://openproblemgarden.org/op/choice_number_of_k_chromatic_graphs_of_bounded_order <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/noel_jonathan_a">Noel</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/coloring">Coloring</a> » <a href="/category/vertex_coloring">Vertex coloring</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 $" /> is a <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-chromatic graph on at most <img class="teximage" src="/files/tex/c6307bea3dbafaf140155114bd35bb788fc000d8.png" alt="$ mk $" /> vertices, then <img class="teximage" src="/files/tex/0d0a9568608331000410c601a041b1c391b31d01.png" alt="$ \text{ch}(G)\leq \text{ch}(K_{m*k}) $" />. </div> </tr></td> </table> </td> </tr> </table> Noel, Jonathan A. choosability complete multipartite graph list coloring Graph Theory Coloring Vertex coloring http://openproblemgarden.org/op/choice_number_of_k_chromatic_graphs_of_bounded_order#comment Sat, 02 Feb 2013 20:28:11 +0100 Jon Noel 44879 at http://openproblemgarden.org