http://openproblemgarden.org/op/faithful_cycle_covers Comments for "Faithful cycle covers" en http://openproblemgarden.org/op/faithful_cycle_covers <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/seymour">Seymour</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/graph_theory">Graph Theory</a> » <a href="/category/basic_graph_theory">Basic G.T.</a> » <a href="/category/cycles_0">Cycles</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; If <img class="teximage" src="/files/tex/5969f28fd067291799f25ca43b6642feb6b04bd0.png" alt="$ G = (V,E) $" /> is a graph, <img class="teximage" src="/files/tex/acf577dca5adcf9fd9f7fb631a68262035044887.png" alt="$ p : E \rightarrow {\mathbb Z} $" /> is admissable, and <img class="teximage" src="/files/tex/fa56cd603dd6dbffa93ed375e6a002107e59c9bb.png" alt="$ p(e) $" /> is even for every <img class="teximage" src="/files/tex/730c5d64c8d749c640adc18eb493c641ff1addc9.png" alt="$ e \in E(G) $" />, then <img class="teximage" src="/files/tex/d9c8f5e55f04622be55791c713068d286259ce27.png" alt="$ (G,p) $" /> has a faithful cover. </div> </tr></td> </table> </td> </tr> </table> Seymour, Paul D. cover cycle Graph Theory Basic Graph Theory Cycles http://openproblemgarden.org/op/faithful_cycle_covers#comment Wed, 07 Mar 2007 13:04:19 +0100 mdevos 140 at http://openproblemgarden.org