http://openproblemgarden.org/op/weighted_colouring_of_hexagonal_graphs Comments for "Weighted colouring of hexagonal graphs." en http://openproblemgarden.org/op/weighted_colouring_of_hexagonal_graphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/mcdiarmid_colin">McDiarmid</a>; <a href="/category/reed_bruce_a">Reed</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; There is an absolute constant <img class="teximage" src="/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png" alt="$ c $" /> such that for every hexagonal graph <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> and vertex weighting <img class="teximage" src="/files/tex/6b14cbdc1cda96520fd87d9507b262f943ccf8ba.png" alt="$ p:V(G)\rightarrow \mathbb{N} $" />, <img class="teximage" src="/files/tex/9b4ccf7620c2a90a97c40177afd9201723864ba8.png" alt="$$\chi(G,p) \leq \frac{9}{8}\omega(G,p) + c $$" /> </div> </tr></td> </table> </td> </tr> </table> McDiarmid, Colin Reed, Bruce A. Graph Theory Coloring Vertex coloring http://openproblemgarden.org/op/weighted_colouring_of_hexagonal_graphs#comment Wed, 13 Mar 2013 19:00:06 +0100 fhavet 47511 at http://openproblemgarden.org