Let $G=(V,E)$ be an acyclic directed graph with source $s \in V$ and sink $t \in V$, $n=|V|,m=|E|$. Is it always true that for every blocking flow $f$ we have $\text{value}(f)\geq \frac{c}{n}$, where $c$ is the value of a maximum $s$-$t$-flow?
I have been sitting at this one for quite a few hours and can't seem to figure it out. As a corollary to a flow decomposition theorem I know that there exist an $s$-$t$ augmenting path which induces a flow of $\frac{c}{m}$ but unfortunately this is not good enough as in directed acyclic graphs $m$ is not tightly bounded by $n$. I also read about Dinic's algorithm and that it shows that $n$ blocking flows are sufficient to generate a maximum flow, but I don't see how I could apply this to the question as these flows are in the residual graph $G_f$. Also it odes not need that $G$ is acyclic.
(A blocking flow $f$ is a flow where $s$ and $t$ are disconnected in the residual graph $G_f$ or alternatively where every $s$-$t$ path contains at least one saturated edge).