How would you prove that the number of cuts in a graph (where cut is a set of edges which split two vertices) cannot be smaller than the number of directed paths from one vertex to the other?
Comparing the number of cuts and paths in graph
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graph-theory
discrete-mathematics
1 Answers
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That would depend on what you know about graphs. Do you know the Max-Flow-Min-Cut theorem?
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1@Ondrej: They are if you assign each edge a capacity of $1$. Specifically, you want to look at [Menger’s theorem](http://en.wikipedia.org/wiki/Menger%27s_Theorem); you may find the last two PDF’s listed under *External links* useful. – 2019-05-17