Let N = (V,A,c,s,t) be a network. Assuming that all minimum s-t cuts in N consist only of edges with integer capacities, then there is an integer maximum flow in N.
I think this should be true because of the max-flow-min-cut theorem ($val_{MAX}(f) = cap(mincut(s-t))$). So all cap of the edges of the mincut are integers, then the whole result must be an integer and therefore the max-flow too. but how can I guarantee that all edges in N that are part of the max-flow are integers?