Computers and Technology, 20.08.2019 22:20 aaroncx4900

Which of the following claims are true and which are false. justify your answer by giving either a (short) proof or a counterexample. (a) in any maximum flow there are no directed cycles that carry positive flow. (a cycle (e1,.ek) carries positive flow iff f(et)> (ek) > 0.) (b) there always exists a maximum flow without cycles carrying positive flow. (c) if all edges in a graph have distinct capacities, there is a unique maximum flow. (d) in a directed graph with at most one edge between each pair of vertices, if we replace each directed edge by an undirected edge, the maximum flow remains unchanged. (e) if we multiply all edge capacities by a positive number a, the minimum cut remains unchan ged.

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Which of the following claims are true and which are false. justify your answer by giving either a (...

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