title: Max Flow/Minimum Cut - Flow after removing K edges algorithm
body: <p>I was asked to develop an algorithm for the following problem :</p>
  <p>Given :</p>
  <ol>
  <li>A flow network G whose edges have maximum capacity of 1</li>
  <li>G's maximum flow |F|</li>
  <li>A positive integer K</li>
  </ol>
  <p>Delete exactly K edges so that the flow of the network is minimized.</p>
  <p>My thoughts/algorithm :</p>
  <ol>
  <li><p>If K is greater than or equal to |F| delete ALL of the edges that cross G's Minimum cut
  and if K is still greater than zero delete <strong>random edges</strong> and the new max flow is zero</p>
  </li>
  <li><p>If K is equal to |F| delete ALL of the edges that cross G's Minimum cut
  and the new max flow is zero</p>
  </li>
  <li><p>If K is less than |F| delete <strong>K</strong> of the edges that cross G's Minimum cut
  and the new max flow is |F|-K</p>
  </li>
  </ol>
  <p>I am in need of some validation as the Max Flow/Min Cut is new to me.
  Lastly the intuition behind the Max Flow/Min Cut that i got is that the Min (Source,Sink) cut works as a <strong>&quot;bottleneck&quot;</strong> to the maximum flow we can push in the network.Is that right?</p>