http://openproblemgarden.org/op/a_homomorphism_problem_for_flows Comments for "A homomorphism problem for flows" en http://openproblemgarden.org/op/a_homomorphism_problem_for_flows <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/devos">DeVos</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/flows">Nowhere-zero flows</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/4bd0590f5618f9306e6f1a2fe10e8b811859c1d9.png" alt="$ M,M&#039; $" /> be abelian groups and let <img class="teximage" src="/files/tex/0841b3f2c65d1f2fa19ef611b62df2cbe21b707b.png" alt="$ B \subseteq M $" /> and <img class="teximage" src="/files/tex/3be253a61ac2430d053b2c331b9d0516305f8116.png" alt="$ B&#039; \subseteq M&#039; $" /> satisfy <img class="teximage" src="/files/tex/44dba92dfcc7e25e513f45325ee83a69a896eb1c.png" alt="$ B=-B $" /> and <img class="teximage" src="/files/tex/8fce1069de40506650f70aa0d0ee79f5a36ed456.png" alt="$ B&#039; = -B&#039; $" />. If there is a <a href="http://en.wikipedia.org/wiki/graph homomorphism">homomorphism</a> from <img class="teximage" src="/files/tex/5264bebd8d0c334fec1533103d0f600b665604c2.png" alt="$ Cayley(M,B) $" /> to <img class="teximage" src="/files/tex/e2d1e39749b1550537591fb4ea1057b69feb5bb0.png" alt="$ Cayley(M&#039;,B&#039;) $" />, then every graph with a B-flow has a B'-flow. </div> </tr></td> </table> </td> </tr> </table> DeVos, Matt homomorphism nowhere-zero flow tension Graph Theory Coloring Nowhere-zero flows http://openproblemgarden.org/op/a_homomorphism_problem_for_flows#comment Wed, 07 Mar 2007 11:43:22 +0100 mdevos 134 at http://openproblemgarden.org