A scaling limit for the length of the longest cycle in a sparse random graph

We discuss the length Lc,n of longest cycle in a sparse random graph Gn,p, p=c/n, c constant. show that for large there exists function f(c) such Lc,n/n?f(c) a.s. The f(c)=1??k=1?pk(c)e?kc where pk(c) is polynomial c. are only able to explicitly give values p1,p2, although we could principle compute any pk. see immediately path also asymptotic f(c)n w.h.p.