True or false. If true provide a short proof, if false give a counterexample: a.

Question

True or false. If true provide a short proof, if false give a counterexample:
a. In any max flow, there is no directed cycle on which every edge carries
positive flow
b. There exists a max flow for which there is no directed cycle on which every
edge carries positive flow
c. If all edge capacities are distinct, the max flow is unique
d. If all edge capacities are increased by an additive constant, the min cut
remains unchanged
e. If all edge capacities are multiplied by a positive integer, the min cut remains
unchanged

Explanation / Answer

a)False

b)True

c)False

d)False

e)True:value of every get multiplied by positive integer.the relative order of flow remains unchanged.

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