title: Second min cost spanning tree
body: <p>I'm writing an algorithm for finding the second min cost spanning tree.  my idea was as follows:</p>
  
  <ol>
  <li>Use kruskals to find lowest MST. </li>
  <li>Delete the lowest cost edge of the MST. </li>
  <li>Run kruskals again on the entire graph. </li>
  <li>return the new MST.</li>
  </ol>
  
  <p>My question is:  Will this work?  Is there a better way perhaps to do this?</p>