http://openproblemgarden.org/op/circular_colouring_the_orthogonality_graph Comments for "Circular colouring the orthogonality graph" en http://openproblemgarden.org/op/circular_colouring_the_orthogonality_graph#comment-6666 <p>I am pretty confident this is still open. Apart from this one many-author paper, I don't think it has received any significant attention. </p> Mon, 28 Sep 2009 09:28:06 +0200 md comment 6666 at http://openproblemgarden.org http://openproblemgarden.org/op/circular_colouring_the_orthogonality_graph#comment-6665 <p>Does anyone know if this problem is still open?</p> Mon, 28 Sep 2009 02:21:59 +0200 Anonymous comment 6665 at http://openproblemgarden.org http://openproblemgarden.org/op/circular_colouring_the_orthogonality_graph#comment-2868 <p>The problem you mention, 10769 of the AMM, concerns the chromatic number of the orthogonality graph. The problem here concerns the <em>circular</em> chromatic number of the orthogonality graph, and I believe it is still open.</p> Tue, 04 Nov 2008 19:15:51 +0100 mdevos comment 2868 at http://openproblemgarden.org http://openproblemgarden.org/op/circular_colouring_the_orthogonality_graph#comment-2866 <p>This is problem 10769 of the American Mathematical Monthly. The solution appeared in AMM 108 (2001), 774-775. See also http://tph.tuwien.ac.at/~svozil/publ/blatter.htm</p> <p>Christian Blatter</p> Tue, 04 Nov 2008 17:14:02 +0100 Anonymous comment 2866 at http://openproblemgarden.org http://openproblemgarden.org/op/circular_colouring_the_orthogonality_graph <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/devos">DeVos</a>; <a href="/category/ghebleh_mohammad">Ghebleh</a>; <a href="/category/goddyn">Goddyn</a>; <a href="/category/mohar">Mohar</a>; <a href="/category/naserasr_reza">Naserasr</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> <p>Let <img class="teximage" src="/files/tex/12c7a1c6d42488a2b1af975bdcce61ec9377b709.png" alt="$ {\mathcal O} $" /> denote the graph with vertex set consisting of all lines through the origin in <img class="teximage" src="/files/tex/5fb08dc0aafafca19601b16cfeff6443d15c3526.png" alt="$ {\mathbb R}^3 $" /> and two vertices adjacent in <img class="teximage" src="/files/tex/12c7a1c6d42488a2b1af975bdcce61ec9377b709.png" alt="$ {\mathcal O} $" /> if they are perpendicular.</p> <div class="envtheorem"><b>Problem</b>&nbsp;&nbsp; Is <img class="teximage" src="/files/tex/ee0ecd597af84da66753671f734858c77288d4be.png" alt="$ \chi_c({\mathcal O}) = 4 $" />? </div> </tr></td> </table> </td> </tr> </table> DeVos, Matt Ghebleh, Mohammad Goddyn, Luis A. Mohar, Bojan Naserasr, Reza circular coloring geometric graph orthogonality Graph Theory Coloring Vertex coloring http://openproblemgarden.org/op/circular_colouring_the_orthogonality_graph#comment Tue, 23 Sep 2008 07:22:07 +0200 mdevos 2040 at http://openproblemgarden.org