Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question

That would depend on what you know about graphs. Do you know the Max-Flow-Min-Cut theorem?

share|cite|improve this answer
Sure, but neither flow nor edge value is relevant. – Ondrej Sotolar Dec 5 '11 at 0:51
@Ondrej: They are if you assign each edge a capacity of $1$. Specifically, you want to look at Menger’s theorem; you may find the last two PDF’s listed under External links useful. – Brian M. Scott Jan 4 '12 at 6:06

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.