Long paths in sparse random graphs
We consider random graphs with n labelled vertices in which edges are chosen independently and with probability c/n. We prove that almost every random graph of this kind contains a path of length ≧(1 -α(c))n where α(c) is an exponentially decreasing function of c. © 1982 Akadémiai Kiadó.
Bollobás, B. (1982). Long paths in sparse random graphs. Combinatorica, 2 (3), 223-228. https://doi.org/10.1007/BF02579230