MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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

Is there any result that relates the minimum degree of a geometric random graph to its k-vertex connectivity? I read papers where they pose the condition $$d_{\rm min} \geq k$$ to imply that the graph is k-connected (vertex connectivity). Is that an approximation or an asymptotic result? In my case, I need, if not an exact result, a lower bound

$$P({\rm graph~is~connected}) \geq f(d_{\rm min}).$$

I could not find references so far.

share|cite|improve this question
up vote 2 down vote accepted

Does this help?

share|cite|improve this answer

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.