title: Is there a minimum spanning tree that does not contain the min/max weighted edge?
body: <p>If we have an (arbitrary) connected undirected graph G, whose edges have <em>distinct</em> weights,</p>
  
  <ol>
  <li>does every MST of G contains the minimum weighted edge?</li>
  <li>is there an MST of G that does not contain the maximum weighted edge?</li>
  </ol>
  
  <p>Also, I'm more thankful if someone can give a hint of the key things one must keep in mind when dealing with such MST questions.</p>
  
  <p>This is a homework problem.  Thanks.</p>