http://openproblemgarden.org/op/turans_problem_for_hypergraphs Comments for "Turán's problem for hypergraphs" en http://openproblemgarden.org/op/turans_problem_for_hypergraphs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/turan_paul">Turan</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/hypergraphs">Hypergraphs</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Every simple <img class="teximage" src="/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png" alt="$ 3 $" />-uniform hypergraph on <img class="teximage" src="/files/tex/f36625fb2086623f510fdcab4f53cd27a419800a.png" alt="$ 3n $" /> vertices which contains no complete <img class="teximage" src="/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png" alt="$ 3 $" />-uniform hypergraph on four vertices has at most <img class="teximage" src="/files/tex/77fae1e209cf2ef781abf9d88573e4981aa00b15.png" alt="$ \frac12 n^2(5n-3) $" /> hyperedges. </div> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Every simple <img class="teximage" src="/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png" alt="$ 3 $" />-uniform hypergraph on <img class="teximage" src="/files/tex/56259815f2fdf87e92dd22e0058206e8e20fb986.png" alt="$ 2n $" /> vertices which contains no complete <img class="teximage" src="/files/tex/4aaf85facb6534fd470edd32dbdb4e28f6218190.png" alt="$ 3 $" />-uniform hypergraph on five vertices has at most <img class="teximage" src="/files/tex/edaf55f28dcd60182c7c9d88572ea01709769bde.png" alt="$ n^2(n-1) $" /> hyperedges. </div> </tr></td> </table> </td> </tr> </table> Turan, Paul Graph Theory Hypergraphs http://openproblemgarden.org/op/turans_problem_for_hypergraphs#comment Mon, 11 Mar 2013 23:40:20 +0100 fhavet 47343 at http://openproblemgarden.org