http://openproblemgarden.org/op/the_crossing_number_of_the_complete_bipartite_graph Comments for "The Crossing Number of the Complete Bipartite Graph" en http://openproblemgarden.org/op/the_crossing_number_of_the_complete_bipartite_graph <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/turan_paul">Turan</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> <p>The crossing number <img class="teximage" src="/files/tex/1c88c74b39c3c8b388e8af0eb6b815eaa7a993c3.png" alt="$ cr(G) $" /> of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is the minimum number of crossings in all drawings of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> in the plane.</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; <img class="teximage" src="/files/tex/aecee36502739c16e07eea1fc64a43a9e95e9374.png" alt="$ \displaystyle cr(K_{m,n}) = \floor{\frac m2} \floor{\frac {m-1}2} \floor{\frac n2} \floor{\frac {n-1}2} $" /> </div> </tr></td> </table> </td> </tr> </table> Turan, Paul complete bipartite graph crossing number Graph Theory Topological Graph Theory Crossing numbers http://openproblemgarden.org/op/the_crossing_number_of_the_complete_bipartite_graph#comment Fri, 11 May 2007 08:42:53 +0200 Robert Samal 310 at http://openproblemgarden.org