http://openproblemgarden.org/op/total_dominator_chromatic_number_of_a_hypercube Comments for "Total Dominator Chromatic Number of a Hypercube" en http://openproblemgarden.org/op/total_dominator_chromatic_number_of_a_hypercube#comment-76069 <p>Since <img class="teximage" src="/files/tex/a3d4b2775508e7005b18a6366b3de2d5e2d4be46.png" alt="$ \chi^t_d(G) \leq \chi(G)+ \gamma(G) $" /> it follows that for large enough <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> the conjecture does not hold by the same token as written in the comment here http://www.openproblemgarden.org/op/total_domination_number_of_a_hypercube</p> Sat, 01 Nov 2014 17:34:52 +0100 azi comment 76069 at http://openproblemgarden.org http://openproblemgarden.org/op/total_dominator_chromatic_number_of_a_hypercube <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/adel_p_kazemi">Adel P. Kazemi</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/coloring">Coloring</a> » <a href="/category/vertex_coloring">Vertex coloring</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; For any integer <img class="teximage" src="/files/tex/cb1ce0e68e63f4a975ec821a7d55cadd7cb94bc5.png" alt="$ n\geq 5 $" />, <img class="teximage" src="/files/tex/cce29403d7100e4a1f212a1fd52834163997805d.png" alt="$ \chi_d^t(Q_n)=2^{n-2}+2 $" />. </div> </tr></td> </table> </td> </tr> </table> Adel P. Kazemi Total dominator chromatic number, hypercube. Graph Theory Coloring Vertex coloring http://openproblemgarden.org/op/total_dominator_chromatic_number_of_a_hypercube#comment Sun, 06 Oct 2013 17:00:59 +0200 Adel P. Kazemi 57908 at http://openproblemgarden.org