http://openproblemgarden.org/op/erdos_faber_lovasz_conjecture Comments for "Erdős–Faber–Lovász conjecture" en http://openproblemgarden.org/op/erdos_faber_lovasz_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/erdos">Erdos</a>; <a href="/category/faber_vance">Faber</a>; <a href="/category/lovasz">Lovasz</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 $" /> is a simple graph which is the union of <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" /> pairwise edge-disjoint complete graphs, each of which has <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" /> vertices, then the chromatic number of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />. </div> </tr></td> </table> </td> </tr> </table> Erdos, Paul Faber, Vance Lovasz, Laszlo chromatic number Graph Theory Coloring Vertex coloring http://openproblemgarden.org/op/erdos_faber_lovasz_conjecture#comment Thu, 22 Aug 2013 21:34:25 +0200 Jon Noel 55984 at http://openproblemgarden.org