http://openproblemgarden.org/op/half_integral_flow_polynomial_values Comments for "Half-integral flow polynomial values" en http://openproblemgarden.org/op/half_integral_flow_polynomial_values <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/mohar">Mohar</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/algebraical_graph_theory">Algebraic G.T.</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>Let <img class="teximage" src="/files/tex/44849b3f1354ffce69af1f9a0d9812471628cb56.png" alt="$ \Phi(G,x) $" /> be the flow polynomial of a graph <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />. So for every positive integer <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />, the value <img class="teximage" src="/files/tex/9b9e2812ff84a54cde31ee88b9df2800f8b5c4ed.png" alt="$ \Phi(G,k) $" /> equals the number of <a href="http://en.wikipedia.org/wiki/nowhere-zero flows">nowhere-zero</a> <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-flows in <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />. </p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; <img class="teximage" src="/files/tex/f92ea960643014765c1c0ed65e6c4c4c4533503c.png" alt="$ \Phi(G,5.5) &gt; 0 $" /> for every 2-edge-connected graph <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />. </div> </tr></td> </table> </td> </tr> </table> Mohar, Bojan nowhere-zero flow Graph Theory Algebraic Graph Theory http://openproblemgarden.org/op/half_integral_flow_polynomial_values#comment Thu, 31 May 2007 00:28:49 +0200 mohar 348 at http://openproblemgarden.org