Intuition behind Max Flow Algorithm

Given :

  1. A flow network G whose edges have capacity of 1
  2. G’s maximum flow |F|
  3. A positive integer K

Delete exactly K edges so that the flow of the network is minimized.

So I was asked to develop an algorithm for this but that’s not the issue.I would like to know if my thoughts are in the right direction because the Max Flow – Min Cut Theorem is new to me.

My thoughts :

  1. 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 random edges and the new max flow is zero

  2. If K is equal to |F| delete ALL of the edges that cross G’s Minimum cut and the new max flow is zero

  3. If K is less than |F| delete K of the edges that cross G’s Minimum cut and the new max flow is |F|-K

Lastly the way that I understand the Max Flow/Min Cut Theorem is that the Min (Source,Sink) cut works as a "bottleneck" to the maximum flow we can push in the network,right?