http://openproblemgarden.org/op/list_colorings_of_edge_critical_graphs Comments for "List colorings of edge-critical graphs" en http://openproblemgarden.org/op/list_colorings_of_edge_critical_graphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/mohar">Mohar</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/edge_coloring">Edge 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; Suppose that <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is a <img class="teximage" src="/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png" alt="$ \Delta $" />-edge-critical graph. Suppose that for each edge <img class="teximage" src="/files/tex/5105762e0c97083905ebf07919c7d4d5ed38dce3.png" alt="$ e $" /> of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />, there is a list <img class="teximage" src="/files/tex/bd0dfc00a21966b9e90231c00dab0d0aa81a0ab0.png" alt="$ L(e) $" /> of <img class="teximage" src="/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png" alt="$ \Delta $" /> colors. Then <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is <img class="teximage" src="/files/tex/73f33398d7e8aa42e6ec25ee2bb4f2b57ed3391a.png" alt="$ L $" />-edge-colorable unless all lists are equal to each other. </div> </tr></td> </table> </td> </tr> </table> Mohar, Bojan edge-coloring list coloring Graph Theory Coloring Edge coloring http://openproblemgarden.org/op/list_colorings_of_edge_critical_graphs#comment Tue, 12 Jun 2007 02:57:05 +0200 Robert Samal 388 at http://openproblemgarden.org