http://openproblemgarden.org/op/asymptotic_distribution_of_form_of_polyhedra Comments for "Asymptotic Distribution of Form of Polyhedra " en http://openproblemgarden.org/op/asymptotic_distribution_of_form_of_polyhedra <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/rudinger_andreas">Rüdinger</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>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Problem</b>&nbsp;&nbsp; Consider the set of all topologically inequivalent polyhedra with <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" /> edges. Define a form parameter for a polyhedron as <img class="teximage" src="/files/tex/85e33eb70cd1ead9d25ddd845e229cfa8d4c937a.png" alt="$ \beta:= v/(k+2) $" /> where <img class="teximage" src="/files/tex/96cbd9a16c6a5eab03815b093b08f3b2db614e9a.png" alt="$ v $" /> is the number of vertices. What is the distribution of <img class="teximage" src="/files/tex/624e933e0823c4484fba477a090a0dfc8aa2fc56.png" alt="$ \beta $" /> for <img class="teximage" src="/files/tex/f17af0206807b43e4ef529e6e21924cfde801683.png" alt="$ k \to \infty $" />? </div> </tr></td> </table> </td> </tr> </table> Rüdinger, Andreas polyhedral graphs, distribution Graph Theory Basic Graph Theory http://openproblemgarden.org/op/asymptotic_distribution_of_form_of_polyhedra#comment Sat, 09 May 2009 21:43:04 +0200 andreasruedinger 36933 at http://openproblemgarden.org