Bipartite graphs and isolated vertices

[simba31415]

Homework Statement

Hello everyone,

I am trying to determine the the threshold function p=p(n) for a random bipartite graph (see http://en.wikipedia.org/wiki/Erdős–Rényi_model for a 'random graph': I am interested in the same idea, but for random bipartite graphs), such that for a random bipartite graph with 2n vertices (n in each vertex set), with edge probability p>p(n) we almost surely have no isolated vertex as $n \to \infty$ and with p<p(n) we almost surely have an isolated vertex.

I am aware that for normal non-bipartite graphs with n vertices, the probability is p(n)=log(n)/n: I suspect in this case the function is something like klog(n)/n: could anyone help me, please? Thankyou ever so much :)

 

[simba31415]

Just thought i'd check again, nobody has any thoughts on this perhaps? :)

 

[simba31415]

Aaanyone? If not, I guess the mods should feel free to close this thread!