I have proven that there is always an augmenting path of capacity at least $\frac{F}{|E|}$. How do I use this to bound the number of rounds given that I use a relation to increase the flow by a fraction of the flow left to go (i.e.):
If the flow after i iterations has size $F_{k}$ then $F_{k+1} \geq F_i + \frac{F-F_k}{|E|}$. I'm attempting to provide an upper bound to the number of iterations and trying to find a clear/explicit bound in terms of $F$. I've reached teh relation: $$ (F_{k+1}-F_k)(|E|) \geq F-F_k $$
Any ideas?