http://openproblemgarden.org/op/point_sets_with_no_empty_pentagon Comments for "Point sets with no empty pentagon" en http://openproblemgarden.org/op/point_sets_with_no_empty_pentagon#comment-93614 <p>Since the chromatic number is always equal or greater than the clique number, the chromatic number of the visibility graph of sets in A is also unbounded.</p> <p>Cibulka, Kyncl and Valtr have also indirectly solved problem 2.</p> Mon, 25 Mar 2019 09:39:50 +0100 Leonard Nguyen Schøyen comment 93614 at http://openproblemgarden.org http://openproblemgarden.org/op/point_sets_with_no_empty_pentagon#comment-75313 <p>Cibulka, Kyncl and Valtr have solved problem 3. They constructed point sets with no empty pentagon, and whose visibility graph has arbitrarily large clique number.</p> <p>Josef Cibulka, Jan Kyncl and Pavel Valtr: On planar point sets with the pentagon property, Proc. SoCG 2013, pp. 81-90. http://dl.acm.org/citation.cfm?id=2462406</p> Sat, 01 Feb 2014 22:41:37 +0100 David Wood comment 75313 at http://openproblemgarden.org http://openproblemgarden.org/op/point_sets_with_no_empty_pentagon <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/wood_david_r">Wood</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/geometry">Geometry</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Problem</b>&nbsp;&nbsp; Classify the point sets with no empty pentagon. </div> </tr></td> </table> </td> </tr> </table> Wood, David R. combinatorial geometry visibility graph Geometry http://openproblemgarden.org/op/point_sets_with_no_empty_pentagon#comment Tue, 14 Dec 2010 00:49:41 +0100 David Wood 37286 at http://openproblemgarden.org