http://openproblemgarden.org/op/end_devouring_rays Comments for "End-Devouring Rays" en http://openproblemgarden.org/op/end_devouring_rays <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>Problem</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> be a graph, <img class="teximage" src="/files/tex/80a4fb3738c5ceba7fa826deb56874dcbfc305a8.png" alt="$ \omega $" /> a countable end of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />, and <img class="teximage" src="/files/tex/fe461893b9f87593e8b79d83455b531cd9f29913.png" alt="$ K $" /> an infinite set of pairwise disjoint <img class="teximage" src="/files/tex/80a4fb3738c5ceba7fa826deb56874dcbfc305a8.png" alt="$ \omega $" />-rays in <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />. Prove that there is a set <img class="teximage" src="/files/tex/68b4ae741aca7464eb90767e39734ba565d96852.png" alt="$ K&#039; $" /> of pairwise disjoint <img class="teximage" src="/files/tex/80a4fb3738c5ceba7fa826deb56874dcbfc305a8.png" alt="$ \omega $" />-rays that devours <img class="teximage" src="/files/tex/80a4fb3738c5ceba7fa826deb56874dcbfc305a8.png" alt="$ \omega $" /> such that the set of starting vertices of rays in <img class="teximage" src="/files/tex/68b4ae741aca7464eb90767e39734ba565d96852.png" alt="$ K&#039; $" /> equals the set of starting vertices of rays in <img class="teximage" src="/files/tex/fe461893b9f87593e8b79d83455b531cd9f29913.png" alt="$ K $" />. </div> </tr></td> </table> </td> </tr> </table> Georgakopoulos, Agelos end ray Graph Theory Infinite Graphs http://openproblemgarden.org/op/end_devouring_rays#comment Sun, 03 Feb 2008 01:02:06 +0100 Agelos 735 at http://openproblemgarden.org