http://openproblemgarden.org/op/petersen_coloring_conjecture Comments for "Petersen coloring conjecture" en http://openproblemgarden.org/op/petersen_coloring_conjecture#comment-7089 <p>It is trivially true for all that are 3-edge-colorable -- which is the vast majority. Among the rest, I checked it using computer and lists of snarks for all graphs upto 34 vertices. (And some more -- e.g. all flower-snarks.) </p> <p>Best wishes, Robert</p> Thu, 24 Nov 2011 17:19:38 +0100 Robert Samal comment 7089 at http://openproblemgarden.org http://openproblemgarden.org/op/petersen_coloring_conjecture#comment-7067 <p>For which bridgeless cubic graphs has this been checked for?</p> Mon, 07 Nov 2011 23:55:19 +0100 Anonymous comment 7067 at http://openproblemgarden.org http://openproblemgarden.org/op/petersen_coloring_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/jaeger">Jaeger</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/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> be a <a href="http://en.wikipedia.org/wiki/cubic graph">cubic</a> graph with no <a href="http://en.wikipedia.org/wiki/bridge (graph theory)">bridge</a>. Then there is a coloring of the edges of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> using the edges of the <a href="http://en.wikipedia.org/wiki/petersen graph">Petersen</a> graph so that any three mutually adjacent edges of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> map to three mutually adjancent edges in the Petersen graph. </div> </tr></td> </table> </td> </tr> </table> Jaeger, Francois cubic edge-coloring Petersen graph Graph Theory Coloring Edge coloring http://openproblemgarden.org/op/petersen_coloring_conjecture#comment Wed, 07 Mar 2007 13:55:25 +0100 mdevos 143 at http://openproblemgarden.org