b---d / \ / \ a / f \ / \ / c e]]>

The following graph have a maximum flow of 1. Is this really the graph you are considering?]]>

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 a-b-d-f 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 Max-Flow in this graph is 2 ( a-b-e-f,a-c-d-f).

It seems that I am missing something here.Can any one tell me how the Ford-Fulkerson Algorithm runs in this Graph ?

Thanx in Advance !]]>