Open Problem Garden - spanning trees - Comments http://openproblemgarden.org/op/spanning_trees Comments for "spanning trees" en Solution by Ruben van der Zwaan (re: spanning trees) http://openproblemgarden.org/op/spanning_trees#comment-6969 <p>Where is the solution posted?</p> Fri, 20 May 2011 23:37:38 +0200 Anonymous comment 6969 at http://openproblemgarden.org definition (re: spanning trees) http://openproblemgarden.org/op/spanning_trees#comment-6756 <p>adjacent to at least one leaf.</p> Sat, 03 Jul 2010 13:57:18 +0200 leshabirukov comment 6756 at http://openproblemgarden.org definition? (re: spanning trees) http://openproblemgarden.org/op/spanning_trees#comment-6755 <p>what is a support vertex?</p> Fri, 02 Jul 2010 17:58:42 +0200 Anonymous comment 6755 at http://openproblemgarden.org spanning trees http://openproblemgarden.org/op/spanning_trees <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></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</b>&nbsp;&nbsp; Prove or disprove: Let <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> be a graph with the minimum vertex degree at least 2; that is, <img class="teximage" src="/files/tex/96ae81fb0087a7e4c2537972b978fb0cfb8a7c59.png" alt="$ \delta(G)\geq 2 $" />. Then there exists a spanning tree <img class="teximage" src="/files/tex/79f55d2e1d83a7726c807a70cbe756713b0437b6.png" alt="$ T $" /> of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> such that for every support vertex <img class="teximage" src="/files/tex/96cbd9a16c6a5eab03815b093b08f3b2db614e9a.png" alt="$ v $" /> in <img class="teximage" src="/files/tex/79f55d2e1d83a7726c807a70cbe756713b0437b6.png" alt="$ T $" /> if <img class="teximage" src="/files/tex/71888edb7df1a28db99d1bb63045685a6a06f9f0.png" alt="$ \deg_G(v)\geq 3 $" />, then <img class="teximage" src="/files/tex/8a6e3c2c3e888b71a237fa0f69ab0002188b5fcb.png" alt="$ \deg_T(v)\geq 3 $" />. </div> </tr></td> </table> </td> </tr> </table> spanning trees Graph Theory http://openproblemgarden.org/op/spanning_trees#comment Fri, 02 Jul 2010 16:41:00 +0200 akhodkar 37231 at http://openproblemgarden.org