Let's assume that for every $e\in E$ it holds that $c(e)$ is an integer. Does it mean that there exists a max flow $f$ that for every $e\in E$ it holds that $f(e)$ is an integer? It sounds obvious but I can't exactly say why it is true.
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2$\begingroup$ Have you ever heard of the max-flow min-cut theorem, the most famous and the most basic theorem in the theory of flow network? Have you ever heard of any algorithm that computes the maximum flow? $\endgroup$– John L.Jan 31, 2022 at 18:20
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