title: heaviest edge with lowest weight between all paths
body: <p>Given a graph with n vertices, indirect,weighted, with no negative cycles and two nodes s,t - to find a path from s to t that the heaviest edge in the path have the lightest weight between all paths from s to t.</p>
  
  <p>one solution I thought about to run BFS from s, find some path between s to t, save the heaviest edge in the path, delete it, and do it at most |E| times.
  the complexity is O(|V| + |E|)*E).
  I'm looking for another solution that maybe involves network flow.</p>
  
  <p>Thanks.</p>