http://openproblemgarden.org/op/5_local_tensions Comments for "5-local-tensions" en http://openproblemgarden.org/op/5_local_tensions <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/devos">DeVos</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/topological_graph_theory">Topological G.T.</a> » <a href="/category/coloring_1">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 exists a fixed constant <img class="teximage" src="/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png" alt="$ c $" /> (probably <img class="teximage" src="/files/tex/b1faa9584556785b57e447d15d1d2178572c5d90.png" alt="$ c=4 $" /> suffices) so that every embedded (loopless) graph with edge-width <img class="teximage" src="/files/tex/4955fa317e705797fabe67a986cb7273813cce12.png" alt="$ \ge c $" /> has a 5-local-tension. </div> </tr></td> </table> </td> </tr> </table> DeVos, Matt coloring surface tension Graph Theory Topological Graph Theory Coloring http://openproblemgarden.org/op/5_local_tensions#comment Fri, 22 Jun 2007 08:30:50 +0200 mdevos 411 at http://openproblemgarden.org