Given :
 A flow network G whose edges have capacity of 1
 G’s maximum flow F
 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 :

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

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

If K is less than F delete K of the edges that cross G’s Minimum cut and the new max flow is FK
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?