Cycles and Unicyclic Components in Random Graphs
Svante Janson · Combinatorics Probability Computing · 2003
The sizes of the cycles and unicyclic components in the random graph , are studied using the language of point processes. This refines several earlier results by different authors. Asymptotic distributions of various random variables are given: these distributions include the gamma distributions with parameters 1/4, 1/2 and 3/4, as well as the Poisson–Dirichlet and GEM distributions with parameters 1/4 and 1/2.