http://openproblemgarden.org/op/3_edge_coloring_conjecture Comments for "3-Edge-Coloring Conjecture" en http://openproblemgarden.org/op/3_edge_coloring_conjecture#comment-93682 <p>Is this conjecture missing some greater context? It seems obviously false on its own</p> Thu, 23 Jun 2022 16:27:00 +0200 Anonymous comment 93682 at http://openproblemgarden.org http://openproblemgarden.org/op/3_edge_coloring_conjecture#comment-93681 <p>wouldn't removing any edge from a cubic graph make the graph not cubic?</p> Wed, 22 Jun 2022 17:35:55 +0200 Anonymous comment 93681 at http://openproblemgarden.org http://openproblemgarden.org/op/3_edge_coloring_conjecture#comment-93668 <p>What would be the cubic graph homeomorphic to K4-e? I think I can show there does not exist a cubic graph homeomorphic to K4-e. If so, this would seem to contradict the conjecture's claim.</p> Tue, 03 Aug 2021 06:31:13 +0200 Anonymous comment 93668 at http://openproblemgarden.org http://openproblemgarden.org/op/3_edge_coloring_conjecture#comment-93653 <p>Hello, I would like to know whether anybody made any progress on this. I tried to google and found nothing. Also, why is there nothing in Bibliography of this problem? Is there any paper involving or proposing it? Thanks in advance</p> Fri, 13 Nov 2020 18:47:38 +0100 Anonymous comment 93653 at http://openproblemgarden.org http://openproblemgarden.org/op/3_edge_coloring_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/arthur">Arthur</a>; <a href="/category/hoffmann_ostenhof">Hoffmann-Ostenhof</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</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 <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> with <img class="teximage" src="/files/tex/ac99a71a6e28acc3052e542089238e810d347be6.png" alt="$ |V(G)|&gt;2 $" /> is a connected cubic graph admitting a <img class="teximage" src="/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png" alt="$ 3 $" />-edge coloring. Then there is an edge <img class="teximage" src="/files/tex/730c5d64c8d749c640adc18eb493c641ff1addc9.png" alt="$ e \in E(G) $" /> such that the cubic graph homeomorphic to <img class="teximage" src="/files/tex/a9c40841d6043b14ca9501d156e86164ad3f81e5.png" alt="$ G-e $" /> has a <img class="teximage" src="/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png" alt="$ 3 $" />-edge coloring. </div> </tr></td> </table> </td> </tr> </table> Arthur Hoffmann-Ostenhof 3-edge coloring 4-flow removable edge Graph Theory http://openproblemgarden.org/op/3_edge_coloring_conjecture#comment Tue, 28 Apr 2020 17:41:20 +0200 arthur 60046 at http://openproblemgarden.org