title: Finding the lowest amount of edges in all minimum cuts in flow network
body: <p>Given a network N, I want to find the minimum cut that has the lowest number of edges in it. I thought about:</p>
  <p>Find the maximum flow (with Dinitz algorithm for example)<br>
  Increase the capacity function such that for every edge e c'(e)=c(e)+1, then use Dinitz algorithm again and calculate the difference.<br>
  That difference will be the minimum number of edges in the mincut.</p>
  <p>But I got stuck proving it.</p>
  <p>Is the concept wrong? Or am I just proving it wrong?</p>