http://openproblemgarden.org/op/hamiltonian_cycles_in_powers_of_infinite_graphs Comments for "Hamiltonian cycles in powers of infinite graphs" en http://openproblemgarden.org/op/hamiltonian_cycles_in_powers_of_infinite_graphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/georgakopoulos_agelos">Georgakopoulos</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/infinite_graphs">Infinite Graphs</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp;<br /> <ol class="enumerate"> \item If <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is a countable connected graph then its third <a href="http://en.wikipedia.org/wiki/Glossary_of_graph_theory#Distance">power</a> is hamiltonian. \item If <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is a 2-connected countable graph then its square is hamiltonian. </ol> </div> </tr></td> </table> </td> </tr> </table> Georgakopoulos, Agelos hamiltonian infinite graph Graph Theory Infinite Graphs http://openproblemgarden.org/op/hamiltonian_cycles_in_powers_of_infinite_graphs#comment Tue, 24 Jul 2007 10:02:32 +0200 Robert Samal 490 at http://openproblemgarden.org