https://www.openproblemgarden.org/op/decomposing_an_eulerian_graph_into_cycles_with_no_two_consecutives_edges_on_a_prescirbed_eulerian_tour Comments for "Decomposing an eulerian graph into cycles with no two consecutives edges on a prescribed eulerian tour." en https://www.openproblemgarden.org/op/decomposing_an_eulerian_graph_into_cycles_with_no_two_consecutives_edges_on_a_prescirbed_eulerian_tour <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/sabidussi_gert">Sabidussi</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; Let <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> be an eulerian graph of minimum degree <img class="teximage" src="/files/tex/1f1498726bb4b7754ca36de46c0ccdd09136d115.png" alt="$ 4 $" />, and let <img class="teximage" src="/files/tex/48948390b5dc5ab9a52c0afaff3e950050be14a2.png" alt="$ W $" /> be an eulerian tour of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />. Then <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> admits a decomposition into cycles none of which contains two consecutive edges of <img class="teximage" src="/files/tex/48948390b5dc5ab9a52c0afaff3e950050be14a2.png" alt="$ W $" />. </div> </tr></td> </table> </td> </tr> </table> Sabidussi, Gert Graph Theory Basic Graph Theory Cycles https://www.openproblemgarden.org/op/decomposing_an_eulerian_graph_into_cycles_with_no_two_consecutives_edges_on_a_prescirbed_eulerian_tour#comment Mon, 04 Mar 2013 06:15:52 +0100 fhavet 46606 at https://www.openproblemgarden.org