title: Adding weights to all edges of graph - change in spanning tree and shortest paths
body: <blockquote>
    <p>(a) Let T be a minimum spanning tree of a weighted graph G. Construct
    a new graph G by adding a weight of k to every edge of G. Do the edges
    of T form a minimum spanning tree of G. Prove the statement or give a
    counterexample.</p>
    
    <p>(b) Let P = {s, . . . , t} describe a shortest weighted path between
    vertices s and t of a weighted graph G. Construct a new graph G by
    adding a weight of k to every edge of G. Does P describe a shortest
    path from s to t in G. Prove the statement or give a counterexample.</p>
  </blockquote>
  
  <p>My solution:</p>
  
  <p>a) Edges of T still form minimum spanning tree of G, since all edge weights are increased by same amount.</p>
  
  <p>b) P still describes shortest path from s to t in G (same reason)</p>
  
  <p>Can someone please verify the answers?</p>