http://openproblemgarden.org/op/fowlers_conjecture_on_eigenvalues_of_3_6_polyhedra Comments for "Fowler's Conjecture on eigenvalues of (3,6)-polyhedra" en http://openproblemgarden.org/op/fowlers_conjecture_on_eigenvalues_of_3_6_polyhedra#comment-343 <p>You can find the proof on the arxiv: </p> <p> Matt DeVos, Luis Goddyn, Bojan Mohar, Robert Samal: <a href="http://www.arxiv.org/abs/0712.1631">Cayley sum graphs and eigenvalues of <img class="teximage" src="/files/tex/54cca356ae4bc518fc2bb0e473f1368b61415fcc.png" alt="$ (3,6) $" />-fullerenes</a> </p> <p>Robert Samal</p> Tue, 08 Apr 2008 01:31:13 +0200 Robert Samal comment 343 at http://openproblemgarden.org http://openproblemgarden.org/op/fowlers_conjecture_on_eigenvalues_of_3_6_polyhedra#comment-184 <p>The proof is solid, but the paper is still in preliminary form.. coming soon!</p> Fri, 07 Sep 2007 06:56:41 +0200 mdevos comment 184 at http://openproblemgarden.org http://openproblemgarden.org/op/fowlers_conjecture_on_eigenvalues_of_3_6_polyhedra#comment-183 <p>What is the status of your possible proof?</p> <p>Gordon Royle </p> Fri, 07 Sep 2007 02:22:08 +0200 Gordon Royle comment 183 at http://openproblemgarden.org http://openproblemgarden.org/op/fowlers_conjecture_on_eigenvalues_of_3_6_polyhedra#comment-17 <p>Together with Luis Goddyn, Bojan Mohar, and Robert Samal, we believe we have solved this conjecture in the affirmative. As soon as there is a paper in the ArXiv, we'll post a link to it here.</p> <p>Matt DeVos</p> Tue, 22 May 2007 06:32:55 +0200 mdevos comment 17 at http://openproblemgarden.org http://openproblemgarden.org/op/fowlers_conjecture_on_eigenvalues_of_3_6_polyhedra <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/fowler">Fowler</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/algebraical_graph_theory">Algebraic G.T.</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> be the graph of a <img class="teximage" src="/files/tex/54cca356ae4bc518fc2bb0e473f1368b61415fcc.png" alt="$ (3,6) $" />-polyhedron with <img class="teximage" src="/files/tex/bb5d192e8d6a16e90cc773b79783d49620f76ede.png" alt="$ 2k + 4 $" /> vertices. Then the eigenvalues of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> can be partitioned into three classes: <img class="teximage" src="/files/tex/acf0918d0c9caeff482349970a3636db0ddfca51.png" alt="$ K = \{3, -1, -1, -1\} $" />, <img class="teximage" src="/files/tex/e613a55348a12a5a8c95a79d7689bfa7ab7435bd.png" alt="$ P = {x_1, ..., x_k\} $" /> (where <img class="teximage" src="/files/tex/dce4936db6220b56450615964eb030778cb2790f.png" alt="$ x_i $" /> is nonnegative for <img class="teximage" src="/files/tex/b2dc2586f78a0a5695206b04bab6ea68dbb0ff46.png" alt="$ i = 1, \dots , k $" />), and <img class="teximage" src="/files/tex/f936c56cf996ce092f80ad0718fb169d863bf1fe.png" alt="$ N = - P $" />. </div> </tr></td> </table> </td> </tr> </table> Fowler, Patrick W. (3,6)-polyhedron eigenvalues Graph Theory Algebraic Graph Theory http://openproblemgarden.org/op/fowlers_conjecture_on_eigenvalues_of_3_6_polyhedra#comment Thu, 19 Apr 2007 03:47:55 +0200 Robert Samal 287 at http://openproblemgarden.org