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Let H be a connected graph and G be a supergraph of H. It is trivial that for any k-flow (D, f) of G, the restriction of (D, f) on the edge subset E(G / H) is a k-flow of the contracted graph G / H. However, the other direction of the question is neither trivial nor straightforward at all: for any k-flow $$(D',f')$$ ( D ′ , f ′ ) of the contracted graph G / H, whether or not the supergraph...
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