http://openproblemgarden.org/op/almost_all_non_hamiltonian_3_regular_graphs_are_1_connected Comments for "Almost all non-Hamiltonian 3-regular graphs are 1-connected" en http://openproblemgarden.org/op/almost_all_non_hamiltonian_3_regular_graphs_are_1_connected <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/haythorpe_michael">Haythorpe</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>Conjecture</b>&nbsp;&nbsp; Denote by <img class="teximage" src="/files/tex/dc7c2bcdf0fdc40cfaa4e4b35d12bfa84042b5f4.png" alt="$ NH(n) $" /> the number of non-Hamiltonian 3-regular graphs of size <img class="teximage" src="/files/tex/56259815f2fdf87e92dd22e0058206e8e20fb986.png" alt="$ 2n $" />, and similarly denote by <img class="teximage" src="/files/tex/f397fa463c02be6928f5ad6655b68aa9a62c7195.png" alt="$ NHB(n) $" /> the number of non-Hamiltonian 3-regular 1-connected graphs of size <img class="teximage" src="/files/tex/56259815f2fdf87e92dd22e0058206e8e20fb986.png" alt="$ 2n $" />.</p> <p>Is it true that <img class="teximage" src="/files/tex/42bbfff98bff9a4b114d982e5a9f8a07ad062a2a.png" alt="$ \lim\limits_{n \rightarrow \infty} \displaystyle\frac{NHB(n)}{NH(n)} = 1 $" />? </div> </tr></td> </table> </td> </tr> </table> Haythorpe, Michael Hamiltonian, Bridge, 3-regular, 1-connected Graph Theory Basic Graph Theory http://openproblemgarden.org/op/almost_all_non_hamiltonian_3_regular_graphs_are_1_connected#comment Fri, 23 Aug 2013 08:34:56 +0200 mhaythorpe 56028 at http://openproblemgarden.org