
Suppose the graph is as follows :
Let it have 6 vertex {a,b,c,d,e,f} where 'a' is source and 'f' is sink. vertex 'a' is connected to vertex 'b'.vertex 'b' is connected to vertex 'd' and 'e'. vertex 'c' is connected to vertex 'd'. vertex 'd' and 'e' are connected to vertex 'f'. All edges have 1 unit capicity.
Now, suppose the Augementing path finding algorithm finds the path abdf in it`s first run. Then there is no other path left in residual graph.So the Max flow in this case will be 1 but actually MaxFlow in this graph is 2 ( abef,acdf).
It seems that I am missing something here.Can any one tell me how the FordFulkerson Algorithm runs in this Graph ?
Thanx in Advance ! 