http://www.openproblemgarden.org/op/sidorenkos_conjecture Comments for "Sidorenko's Conjecture" en http://www.openproblemgarden.org/op/sidorenkos_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/sidorenko_a">Sidorenko</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</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 bipartite graph <img class="teximage" src="/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png" alt="$ H $" /> and graph <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />, the number of homomorphisms from <img class="teximage" src="/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png" alt="$ H $" /> to <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> is at least <img class="teximage" src="/files/tex/a6c4d985a1ddfc6c35b74c9ae8e23d64f97d7781.png" alt="$ \left(\frac{2|E(G)|}{|V(G)|^2}\right)^{|E(H)|}|V(G)|^{|V(H)|} $" />. </div> </tr></td> </table> </td> </tr> </table> Sidorenko, A. density problems extremal combinatorics homomorphism Graph Theory http://www.openproblemgarden.org/op/sidorenkos_conjecture#comment Thu, 10 Oct 2019 10:37:03 +0200 Jon Noel 60039 at http://www.openproblemgarden.org