http://openproblemgarden.org/op/jones_conjecture Comments for "Jones' conjecture" en http://openproblemgarden.org/op/jones_conjecture#comment-93632 <p>Proved for subcubic planar graphs by Marthe Bonamy, François Dross, Tomáš Masařík, Wojciech Nadara, Marcin Pilipczuk, Michał Pilipczuk [https://arxiv.org/abs/1912.01570].</p> Thu, 05 Dec 2019 00:16:33 +0100 David Wood comment 93632 at http://openproblemgarden.org http://openproblemgarden.org/op/jones_conjecture#comment-259 <p>I am Jones. My Taiwanese name is Chuan-Min Lee. This conjecture came up when I was working on it with Ton Kloks and Jiping Liu. I used the name "Jones" instead of my Taiwanese name for ease of communication.</p> Fri, 16 Nov 2007 03:50:12 +0100 Anonymous comment 259 at http://openproblemgarden.org http://openproblemgarden.org/op/jones_conjecture#comment-256 <p>Does anyone know why this is called Jones' Conjecture?</p> Mon, 29 Oct 2007 20:58:42 +0100 Anonymous comment 256 at http://openproblemgarden.org http://openproblemgarden.org/op/jones_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/kloks_ton">Kloks</a>; <a href="/category/lee_chuan_min">Lee</a>; <a href="/category/liu_jiping">Liu</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/basic_graph_theory">Basic G.T.</a> » <a href="/category/cycles_0">Cycles</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>For a graph <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />, let <img class="teximage" src="/files/tex/b13bee1abf89129386621b00fdf272a5bbe6f338.png" alt="$ cp(G) $" /> denote the cardinality of a maximum cycle packing (collection of vertex disjoint cycles) and let <img class="teximage" src="/files/tex/1dd7a4159e23f45f8852b2d9cbc1edcd2b188530.png" alt="$ cc(G) $" /> denote the cardinality of a minimum feedback vertex set (set of vertices <img class="teximage" src="/files/tex/302cdeba125e821f3406302c9789229d48f42ea7.png" alt="$ X $" /> so that <img class="teximage" src="/files/tex/0dd96fb490efee768188f9c7f0da8436d5e5337c.png" alt="$ G-X $" /> is acyclic). </p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; For every planar graph <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />, <img class="teximage" src="/files/tex/c3407aab8c5dd67b27ec62b418dcd71d7b6fb886.png" alt="$ cc(G)\leq 2cp(G) $" />. </div> </tr></td> </table> </td> </tr> </table> Kloks, Ton Lee, Chuan-Min Liu, Jiping cycle packing feedback vertex set planar graph Graph Theory Basic Graph Theory Cycles http://openproblemgarden.org/op/jones_conjecture#comment Tue, 09 Oct 2007 04:11:45 +0200 cmlee 638 at http://openproblemgarden.org