ford fulkerson – Min-cut in a zero flow network from source to well

The max-cut min-flow theorem ensures that the minimum cut of a directed network is equal to the maximum throughput. And we can calculate $$S$$ and $$T$$, are disjoint subsets containing the source and receiver nodes of the residual graph, respectively.

What will be $$S$$ and $$T$$ if the maximum flow from the source to the well is equal to 0, there is no path led from $$s$$ at $$t$$? is $$S$$ is going to be the singleton set {s} or its empty set $$phi$$ and $$T$$ to be the set of summits $$V$$?

In a Min-Cut problem, how often do I have to run Karger's algorithm in a given set of nodes?

Question:

On 22 nodes, how many times do I have to run Karger's algorithm to find a min-cut problem in an error range (for example, <2 or between 0 and 1)?

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Confusion about Min-Cut probabilities

• Watching a video on Counting Minimum Cuts by Tim Roughgarden.
• $$(A_ {i}, B_ {i}) = big ((A_ {1}, B_ {1}), …, (A_ {t}, B_ {t}) big) forall i in Bbb {R}$$
• $$P big ((A_ {i}, B_ {i}) big) geq frac {1} { begin {pmatrix} n \ 2 end {pmatrix}} = p$$, which I interpret as the lower limit of the probability of having at least a minimal reduction.
• In the following problem, two answers A and B are highlighted as correct. I understand why A is correct but I am puzzled why B is also marked as correct.
• A: for each graph $$G$$ with $$n$$ knots and every min cut $$(A, B)$$ (I'm assuming the same thing as $$(A_ {i}, B_ {i})$$) $$P big ((A, B) big) geq p$$.
• B There is a graph $$G$$ with $$n$$ knots and a min cut $$(A, B)$$ (still assuming the same thing as $$(A_ {i}, B_ {i})$$) of $$G$$ such as $$P big ((A, B) big) leq p$$.
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