title: unique minimum spanning tree sufficient and necessary conditions
body: <p>Given a graph G,which are the sufficient and necessary conditions , so that this graph has a unique minimum spanning tree?In addition , how can I proove these conditions?</p>
  
  <p>So far , I  had found that those conditions are :</p>
  
  <p>1)For every partition of V(G) into two subsets, the minimum weight edge with one endpoint in each subset is unique.</p>
  
  <p>2)The maximum-weight edge in any cycle of G is unique.</p>
  
  <p>But I am not sure if this is correct.Even in case this is correct,I cannot prove its correctness.</p>