graph theory – Potential flow and impact vectors

Let $ f $ to be a function on the arc game $ A $ of an acyclic network $ N (x, y) $ (right here $ x $ is the source and $ y $ l & # 39; sink). assume $ 0 leq f (a) leq c (a) $ for everyone $ a in A $ ($ c $ is the capacity function). CA watch $ f $ is a flow if and only if it is a non-negative linear combination of vectors of incidence of $ (x, y) $paths.