Suppose we have an Erdos random graph with $n$ vertices and $c n$ edges.
What can you say about the probability that the graph is connected?
(More importantly) If it is connected, what is the distribution on the number of bridges?
I am interested in asymptotics as $c$ is fixed but $n \rightarrow \infty$. That is, I know that the probability that the graph is connected is exponentially small in $n$, but I don't know what the exponent is.
As for the number of non-bridges, I would like some result like the number of bridges for a random connected graph is $> c' n$ where $c'$ is another constant, with probability approaching $1$.