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By Menger's theorem the maximum number of arc-disjoint paths from a vertex s to a vertex t in a directed graph equals the minumum number of arcs needed to disconnect s and t, i.e., the minimum size of an s-t-cut. The max-flow problem in a network with unit capacities is equivalent to the arc-disjoint paths problem. Moreover the max-flow and min-cut problems form a strongly dual pair. We relax the disjointedness requirement on the paths, allowing them to be almost disjoint, meaning they mayarXiv:2202.10090v1 fatcat:asogjnvgdjg5rkhb446p2cjxwe